Math for max and min x and y of an ellipseConversion from Standard Ellipse Function to General Ellipse...
How would an energy-based "projectile" blow up a spaceship?
A running toilet that stops itself
Is there a math expression equivalent to the conditional ternary operator?
What is Tony Stark injecting into himself in Iron Man 3?
Can Witch Sight see through Mirror Image?
Short SF story. Females use stingers to implant eggs in yearfathers
How to make sure I'm assertive enough in contact with subordinates?
Generating a list with duplicate entries
I am the person who abides by rules but breaks the rules . Who am I
Why do we call complex numbers “numbers” but we don’t consider 2-vectors numbers?
How to recover against Snake as a heavyweight character?
Where is the License file location for Identity Server in Sitecore 9.1?
Precision notation for voltmeters
Paper published similar to PhD thesis
Inorganic chemistry handbook with reaction lists
Propulsion Systems
Why does a car's steering wheel get lighter with increasing speed
Is this Paypal Github SDK reference really a dangerous site?
Exempt portion of equation line from aligning?
Is there a logarithm base for which the logarithm becomes an identity function?
Unfamiliar notation in Diabelli's "Duet in D" for piano
What does it take to become a wilderness skills guide as a business?
Ultrafilters as a double dual
3.5% Interest Student Loan or use all of my savings on Tuition?
Math for max and min x and y of an ellipse
Conversion from Standard Ellipse Function to General Ellipse FunctionNumber of ellipses to uniquely define a co-centered circumscribing ellipsePartial Integral of an ellipseArea of ellipse not in xy-planeFind foci and eccentricity of ellipse given either 5 points or its general equationWhy does the Ellipsograph/Trammel of Archimedes draw an ellipse, really?A new property of conics?1st and 2nd derivative test of max-minI got 5 ellipse parameters, 4 of which are coordinates of 2 focus points, what would the last one be? And how can I get the ellipse function?Parametrization of a rotated ellipse
$begingroup$
I see that the general equation of an ellipse centered at the origin is:
(𝑎𝑥+𝑏𝑦)² + (𝑐𝑥+𝑑𝑦)² = 𝑟²
How do a, b, c, d relate to the coefficients of the general form?
A𝑥² + B𝑥𝑦 + C𝑦² + D𝑥 + E𝑦 + F = 0
After some naive observation I believe:
A = (𝑎² + 𝑐²)
B = 2(𝑎𝑏 + 𝑐𝑑)
C = (𝑏² + 𝑑²)
F = -𝑟²
Pretty sure it's more complicated than that. The issue for me is to do the calculations based on numerical values for an ellipse in either standard or canonical form, as opposed to pencil and paper derivatives.
conic-sections maxima-minima
asked yesterday
TJ SartainTJ Sartain
111
New contributor
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I see that the general equation of an ellipse centered at the origin is:
(𝑎𝑥+𝑏𝑦)² + (𝑐𝑥+𝑑𝑦)² = 𝑟²
How do a, b, c, d relate to the coefficients of the general form?
A𝑥² + B𝑥𝑦 + C𝑦² + D𝑥 + E𝑦 + F = 0
After some naive observation I believe:
A = (𝑎² + 𝑐²)
B = 2(𝑎𝑏 + 𝑐𝑑)
C = (𝑏² + 𝑑²)
F = -𝑟²
Pretty sure it's more complicated than that. The issue for me is to do the calculations based on numerical values for an ellipse in either standard or canonical form, as opposed to pencil and paper derivatives.
conic-sections maxima-minima
asked yesterday
TJ SartainTJ Sartain
111
New contributor
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
have an example $21x^2-6xy+29y^2+6x-58y+151=0$
$endgroup$
– jacky
yesterday
$begingroup$
OK, so using that example, F is an imaginary number. Also, I'm trying to go from the general form (with the capital letters) and get to a, b, c, d, and r.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
I misrepresented my question from the very first line! Basically, I have an ellipse that is not necessarily centered at the origin and possibly rotated. I have either the standard form (or the canonical form as it is derivable) and I am trying to find the max and min x and y.
$endgroup$
– TJ Sartain
yesterday
add a comment |
$begingroup$
I see that the general equation of an ellipse centered at the origin is:
(𝑎𝑥+𝑏𝑦)² + (𝑐𝑥+𝑑𝑦)² = 𝑟²
How do a, b, c, d relate to the coefficients of the general form?
A𝑥² + B𝑥𝑦 + C𝑦² + D𝑥 + E𝑦 + F = 0
After some naive observation I believe:
A = (𝑎² + 𝑐²)
B = 2(𝑎𝑏 + 𝑐𝑑)
C = (𝑏² + 𝑑²)
F = -𝑟²
Pretty sure it's more complicated than that. The issue for me is to do the calculations based on numerical values for an ellipse in either standard or canonical form, as opposed to pencil and paper derivatives.
conic-sections maxima-minima
asked yesterday
TJ SartainTJ Sartain
111
New contributor
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I see that the general equation of an ellipse centered at the origin is:
(𝑎𝑥+𝑏𝑦)² + (𝑐𝑥+𝑑𝑦)² = 𝑟²
How do a, b, c, d relate to the coefficients of the general form?
A𝑥² + B𝑥𝑦 + C𝑦² + D𝑥 + E𝑦 + F = 0
After some naive observation I believe:
A = (𝑎² + 𝑐²)
B = 2(𝑎𝑏 + 𝑐𝑑)
C = (𝑏² + 𝑑²)
F = -𝑟²
Pretty sure it's more complicated than that. The issue for me is to do the calculations based on numerical values for an ellipse in either standard or canonical form, as opposed to pencil and paper derivatives.
conic-sections maxima-minima
conic-sections maxima-minima
asked yesterday
TJ SartainTJ Sartain
111
New contributor
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
TJ SartainTJ Sartain
111
New contributor
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
TJ SartainTJ Sartain
111
New contributor
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
TJ SartainTJ Sartain
111
asked yesterday
TJ SartainTJ Sartain
111
111
New contributor
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
TJ Sartain is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
have an example $21x^2-6xy+29y^2+6x-58y+151=0$
$endgroup$
– jacky
yesterday
$begingroup$
OK, so using that example, F is an imaginary number. Also, I'm trying to go from the general form (with the capital letters) and get to a, b, c, d, and r.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
I misrepresented my question from the very first line! Basically, I have an ellipse that is not necessarily centered at the origin and possibly rotated. I have either the standard form (or the canonical form as it is derivable) and I am trying to find the max and min x and y.
$endgroup$
– TJ Sartain
yesterday
add a comment |
$begingroup$
have an example $21x^2-6xy+29y^2+6x-58y+151=0$
$endgroup$
– jacky
yesterday
$begingroup$
OK, so using that example, F is an imaginary number. Also, I'm trying to go from the general form (with the capital letters) and get to a, b, c, d, and r.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
I misrepresented my question from the very first line! Basically, I have an ellipse that is not necessarily centered at the origin and possibly rotated. I have either the standard form (or the canonical form as it is derivable) and I am trying to find the max and min x and y.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
have an example $21x^2-6xy+29y^2+6x-58y+151=0$
$endgroup$
– jacky
yesterday
$begingroup$
have an example $21x^2-6xy+29y^2+6x-58y+151=0$
$endgroup$
– jacky
yesterday
$begingroup$
OK, so using that example, F is an imaginary number. Also, I'm trying to go from the general form (with the capital letters) and get to a, b, c, d, and r.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
OK, so using that example, F is an imaginary number. Also, I'm trying to go from the general form (with the capital letters) and get to a, b, c, d, and r.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
I misrepresented my question from the very first line! Basically, I have an ellipse that is not necessarily centered at the origin and possibly rotated. I have either the standard form (or the canonical form as it is derivable) and I am trying to find the max and min x and y.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
I misrepresented my question from the very first line! Basically, I have an ellipse that is not necessarily centered at the origin and possibly rotated. I have either the standard form (or the canonical form as it is derivable) and I am trying to find the max and min x and y.
$endgroup$
– TJ Sartain
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$$(ax+by)^2+(cx+dy)^2=r^2\
a^2x^2+2abxy+b^2y^2+c^2x^2+2cdxy+d^2y^2=r^2\
(a^2+c^2)x^2+(2ab+2cd)xy+(b^2+d^2)y^2-r^2=0\
therefore A=a^2+c^2B=2(ab+cd),C=(b^2+d^2),D=E=0,F=-r^2$$
answered yesterday
hokoxixehokoxixe
112
New contributor
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
This is what the OP wrote...
$endgroup$
– Peter Foreman
yesterday
$begingroup$
How do i convert it into $21x^2-6xy+29y^2+6x-58y+151=0$ standard form, I mean $pX^2+qY^2=1$ form
$endgroup$
– jacky
yesterday
$begingroup$
@PeterForeman The OP also said he thought it was more complicated than that. This answers the question, as I read it, and proves that it is not more complicated than that.
$endgroup$
– John Douma
yesterday
$begingroup$
Thanks, that IS how I got to the equivalencies I posted. But I have an equation where D and E are not 0. That's where I suspected there might be more to it. I would be surprised if I could simply ignore D and E but if someone actually verified that, I would accept it.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
@TJSartain If $D$ and $E$ are not zero, then you therefore are dealing with something other than an ellipse centred at the origin.
$endgroup$
– Théophile
yesterday
|
show 2 more comments
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
TJ Sartain is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3139304%2fmath-for-max-and-min-x-and-y-of-an-ellipse%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$$(ax+by)^2+(cx+dy)^2=r^2\
a^2x^2+2abxy+b^2y^2+c^2x^2+2cdxy+d^2y^2=r^2\
(a^2+c^2)x^2+(2ab+2cd)xy+(b^2+d^2)y^2-r^2=0\
therefore A=a^2+c^2B=2(ab+cd),C=(b^2+d^2),D=E=0,F=-r^2$$
answered yesterday
hokoxixehokoxixe
112
New contributor
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
This is what the OP wrote...
$endgroup$
– Peter Foreman
yesterday
$begingroup$
How do i convert it into $21x^2-6xy+29y^2+6x-58y+151=0$ standard form, I mean $pX^2+qY^2=1$ form
$endgroup$
– jacky
yesterday
$begingroup$
@PeterForeman The OP also said he thought it was more complicated than that. This answers the question, as I read it, and proves that it is not more complicated than that.
$endgroup$
– John Douma
yesterday
$begingroup$
Thanks, that IS how I got to the equivalencies I posted. But I have an equation where D and E are not 0. That's where I suspected there might be more to it. I would be surprised if I could simply ignore D and E but if someone actually verified that, I would accept it.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
@TJSartain If $D$ and $E$ are not zero, then you therefore are dealing with something other than an ellipse centred at the origin.
$endgroup$
– Théophile
yesterday
|
show 2 more comments
$begingroup$
$$(ax+by)^2+(cx+dy)^2=r^2\
a^2x^2+2abxy+b^2y^2+c^2x^2+2cdxy+d^2y^2=r^2\
(a^2+c^2)x^2+(2ab+2cd)xy+(b^2+d^2)y^2-r^2=0\
therefore A=a^2+c^2B=2(ab+cd),C=(b^2+d^2),D=E=0,F=-r^2$$
answered yesterday
hokoxixehokoxixe
112
New contributor
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
This is what the OP wrote...
$endgroup$
– Peter Foreman
yesterday
$begingroup$
How do i convert it into $21x^2-6xy+29y^2+6x-58y+151=0$ standard form, I mean $pX^2+qY^2=1$ form
$endgroup$
– jacky
yesterday
$begingroup$
@PeterForeman The OP also said he thought it was more complicated than that. This answers the question, as I read it, and proves that it is not more complicated than that.
$endgroup$
– John Douma
yesterday
$begingroup$
Thanks, that IS how I got to the equivalencies I posted. But I have an equation where D and E are not 0. That's where I suspected there might be more to it. I would be surprised if I could simply ignore D and E but if someone actually verified that, I would accept it.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
@TJSartain If $D$ and $E$ are not zero, then you therefore are dealing with something other than an ellipse centred at the origin.
$endgroup$
– Théophile
yesterday
|
show 2 more comments
$begingroup$
$$(ax+by)^2+(cx+dy)^2=r^2\
a^2x^2+2abxy+b^2y^2+c^2x^2+2cdxy+d^2y^2=r^2\
(a^2+c^2)x^2+(2ab+2cd)xy+(b^2+d^2)y^2-r^2=0\
therefore A=a^2+c^2B=2(ab+cd),C=(b^2+d^2),D=E=0,F=-r^2$$
answered yesterday
hokoxixehokoxixe
112
New contributor
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$$(ax+by)^2+(cx+dy)^2=r^2\
a^2x^2+2abxy+b^2y^2+c^2x^2+2cdxy+d^2y^2=r^2\
(a^2+c^2)x^2+(2ab+2cd)xy+(b^2+d^2)y^2-r^2=0\
therefore A=a^2+c^2B=2(ab+cd),C=(b^2+d^2),D=E=0,F=-r^2$$
answered yesterday
hokoxixehokoxixe
112
New contributor
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered yesterday
hokoxixehokoxixe
112
New contributor
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered yesterday
hokoxixehokoxixe
112
answered yesterday
hokoxixehokoxixe
112
112
New contributor
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
hokoxixe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
This is what the OP wrote...
$endgroup$
– Peter Foreman
yesterday
$begingroup$
How do i convert it into $21x^2-6xy+29y^2+6x-58y+151=0$ standard form, I mean $pX^2+qY^2=1$ form
$endgroup$
– jacky
yesterday
$begingroup$
@PeterForeman The OP also said he thought it was more complicated than that. This answers the question, as I read it, and proves that it is not more complicated than that.
$endgroup$
– John Douma
yesterday
$begingroup$
Thanks, that IS how I got to the equivalencies I posted. But I have an equation where D and E are not 0. That's where I suspected there might be more to it. I would be surprised if I could simply ignore D and E but if someone actually verified that, I would accept it.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
@TJSartain If $D$ and $E$ are not zero, then you therefore are dealing with something other than an ellipse centred at the origin.
$endgroup$
– Théophile
yesterday
|
show 2 more comments
1
$begingroup$
This is what the OP wrote...
$endgroup$
– Peter Foreman
yesterday
$begingroup$
How do i convert it into $21x^2-6xy+29y^2+6x-58y+151=0$ standard form, I mean $pX^2+qY^2=1$ form
$endgroup$
– jacky
yesterday
$begingroup$
@PeterForeman The OP also said he thought it was more complicated than that. This answers the question, as I read it, and proves that it is not more complicated than that.
$endgroup$
– John Douma
yesterday
$begingroup$
Thanks, that IS how I got to the equivalencies I posted. But I have an equation where D and E are not 0. That's where I suspected there might be more to it. I would be surprised if I could simply ignore D and E but if someone actually verified that, I would accept it.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
@TJSartain If $D$ and $E$ are not zero, then you therefore are dealing with something other than an ellipse centred at the origin.
$endgroup$
– Théophile
yesterday
1
1
$begingroup$
This is what the OP wrote...
$endgroup$
– Peter Foreman
yesterday
$begingroup$
This is what the OP wrote...
$endgroup$
– Peter Foreman
yesterday
$begingroup$
How do i convert it into $21x^2-6xy+29y^2+6x-58y+151=0$ standard form, I mean $pX^2+qY^2=1$ form
$endgroup$
– jacky
yesterday
$begingroup$
How do i convert it into $21x^2-6xy+29y^2+6x-58y+151=0$ standard form, I mean $pX^2+qY^2=1$ form
$endgroup$
– jacky
yesterday
$begingroup$
@PeterForeman The OP also said he thought it was more complicated than that. This answers the question, as I read it, and proves that it is not more complicated than that.
$endgroup$
– John Douma
yesterday
$begingroup$
@PeterForeman The OP also said he thought it was more complicated than that. This answers the question, as I read it, and proves that it is not more complicated than that.
$endgroup$
– John Douma
yesterday
$begingroup$
Thanks, that IS how I got to the equivalencies I posted. But I have an equation where D and E are not 0. That's where I suspected there might be more to it. I would be surprised if I could simply ignore D and E but if someone actually verified that, I would accept it.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
Thanks, that IS how I got to the equivalencies I posted. But I have an equation where D and E are not 0. That's where I suspected there might be more to it. I would be surprised if I could simply ignore D and E but if someone actually verified that, I would accept it.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
@TJSartain If $D$ and $E$ are not zero, then you therefore are dealing with something other than an ellipse centred at the origin.
$endgroup$
– Théophile
yesterday
$begingroup$
@TJSartain If $D$ and $E$ are not zero, then you therefore are dealing with something other than an ellipse centred at the origin.
$endgroup$
– Théophile
yesterday
|
show 2 more comments
TJ Sartain is a new contributor. Be nice, and check out our Code of Conduct.
TJ Sartain is a new contributor. Be nice, and check out our Code of Conduct.
TJ Sartain is a new contributor. Be nice, and check out our Code of Conduct.
TJ Sartain is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3139304%2fmath-for-max-and-min-x-and-y-of-an-ellipse%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
have an example $21x^2-6xy+29y^2+6x-58y+151=0$
$endgroup$
– jacky
yesterday
$begingroup$
OK, so using that example, F is an imaginary number. Also, I'm trying to go from the general form (with the capital letters) and get to a, b, c, d, and r.
$endgroup$
– TJ Sartain
yesterday
$begingroup$
I misrepresented my question from the very first line! Basically, I have an ellipse that is not necessarily centered at the origin and possibly rotated. I have either the standard form (or the canonical form as it is derivable) and I am trying to find the max and min x and y.
$endgroup$
– TJ Sartain
yesterday