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Ellipse and triangle

0

$begingroup$

Find the sides $a$, $b$ and $c$ of the triangle ($c=b$) of minimal area circumscribed around ellipse, whose equation is ${x^2over9} + {y^2over4} = 1$, if side $a$ is parallel to $x$-axis.

I suppose that ellipse tangents are side $b$ and $c$. I have that $b=c=sqrt{63}$ and $a=sqrt{108}$, but I am not sure about that.

real-analysis optimization

share|cite|improve this question

edited Mar 23 at 22:40

Rócherz

3,0263823

asked Mar 23 at 21:53

m2017mm2017m

94

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What tringle is referred to by the word "equilateral" in the title?
  $endgroup$
  – user
  Mar 23 at 21:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  sorry, that was mistake
  $endgroup$
  – m2017m
  Mar 23 at 22:01
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  Hint. If you scale the $x$ axis by an appropriate fraction you turn the ellipse into a circle and scale all areas by the same fraction. Find the minimal area triangle for the circle and scale back.
  $endgroup$
  – Ethan Bolker
  Mar 23 at 22:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have got $a=3sqrt3$ and $b=c=frac32sqrt7$. Seems to be 2 times less than your values. Does it help?
  $endgroup$
  – user
  Mar 23 at 22:08
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

Find the sides $a$, $b$ and $c$ of the triangle ($c=b$) of minimal area circumscribed around ellipse, whose equation is ${x^2over9} + {y^2over4} = 1$, if side $a$ is parallel to $x$-axis.

I suppose that ellipse tangents are side $b$ and $c$. I have that $b=c=sqrt{63}$ and $a=sqrt{108}$, but I am not sure about that.

real-analysis optimization

share|cite|improve this question

edited Mar 23 at 22:40

Rócherz

3,0263823

asked Mar 23 at 21:53

m2017mm2017m

94

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What tringle is referred to by the word "equilateral" in the title?
  $endgroup$
  – user
  Mar 23 at 21:56
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  sorry, that was mistake
  $endgroup$
  – m2017m
  Mar 23 at 22:01
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  Hint. If you scale the $x$ axis by an appropriate fraction you turn the ellipse into a circle and scale all areas by the same fraction. Find the minimal area triangle for the circle and scale back.
  $endgroup$
  – Ethan Bolker
  Mar 23 at 22:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have got $a=3sqrt3$ and $b=c=frac32sqrt7$. Seems to be 2 times less than your values. Does it help?
  $endgroup$
  – user
  Mar 23 at 22:08
  
  
  

  
  
  
  

add a comment | 

$begingroup$

Find the sides $a$, $b$ and $c$ of the triangle ($c=b$) of minimal area circumscribed around ellipse, whose equation is ${x^2over9} + {y^2over4} = 1$, if side $a$ is parallel to $x$-axis.

I suppose that ellipse tangents are side $b$ and $c$. I have that $b=c=sqrt{63}$ and $a=sqrt{108}$, but I am not sure about that.

real-analysis optimization

share|cite|improve this question

edited Mar 23 at 22:40

Rócherz

3,0263823

asked Mar 23 at 21:53

m2017mm2017m

94

$endgroup$

share|cite|improve this question

edited Mar 23 at 22:40

Rócherz

3,0263823

asked Mar 23 at 21:53

m2017mm2017m

94

share|cite|improve this question

edited Mar 23 at 22:40

Rócherz

3,0263823

asked Mar 23 at 21:53

m2017mm2017m

94

edited Mar 23 at 22:40

Rócherz

3,0263823

edited Mar 23 at 22:40

Rócherz

3,0263823

asked Mar 23 at 21:53

m2017mm2017m

94

asked Mar 23 at 21:53

m2017mm2017m

94