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Chord of contact in polar coordinate

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Can you please help me to derive the equation of chord of contact for a circle in polar coordinate? I have found the equation in cartesian coordinate but I cannot map that into the polar coordinate. Any help would be appreciated.

Let suppose we want to derive the chord of contact that connects two points, e.g., $A(-pi/3,1)$ and $B(pi/4,1)$ on the unit circle. Center of the circle is $(0,0)$.

All the best,

Russell

geometry trigonometry

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edited Mar 20 at 1:22

Saad

20.4k92352

asked Mar 20 at 0:54

NarimaniNarimani

1

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  If you have the equation in Cartesian coordinates, can't you put $x = rcostheta$ and $y=rsintheta$ to get the equation in polar coordinates?
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  – Minus One-Twelfth
  Mar 20 at 0:57
  

  
  
  
  


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  It’s not very hard to determine the distance of the line from the origin and its direction directly in polar coordinates. From there, it’s a simple matter of plugging the numbers into one of the two standard polar equations of lines.
  $endgroup$
  – amd
  Mar 20 at 1:19
  

  
  
  
  

add a comment | 

0

$begingroup$

Can you please help me to derive the equation of chord of contact for a circle in polar coordinate? I have found the equation in cartesian coordinate but I cannot map that into the polar coordinate. Any help would be appreciated.

Let suppose we want to derive the chord of contact that connects two points, e.g., $A(-pi/3,1)$ and $B(pi/4,1)$ on the unit circle. Center of the circle is $(0,0)$.

All the best,

Russell

geometry trigonometry

share|cite|improve this question

edited Mar 20 at 1:22

Saad

20.4k92352

asked Mar 20 at 0:54

NarimaniNarimani

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If you have the equation in Cartesian coordinates, can't you put $x = rcostheta$ and $y=rsintheta$ to get the equation in polar coordinates?
  $endgroup$
  – Minus One-Twelfth
  Mar 20 at 0:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It’s not very hard to determine the distance of the line from the origin and its direction directly in polar coordinates. From there, it’s a simple matter of plugging the numbers into one of the two standard polar equations of lines.
  $endgroup$
  – amd
  Mar 20 at 1:19
  

  
  
  
  

add a comment | 

$begingroup$

Can you please help me to derive the equation of chord of contact for a circle in polar coordinate? I have found the equation in cartesian coordinate but I cannot map that into the polar coordinate. Any help would be appreciated.

Let suppose we want to derive the chord of contact that connects two points, e.g., $A(-pi/3,1)$ and $B(pi/4,1)$ on the unit circle. Center of the circle is $(0,0)$.

All the best,

Russell

geometry trigonometry

share|cite|improve this question

edited Mar 20 at 1:22

Saad

20.4k92352

asked Mar 20 at 0:54

NarimaniNarimani

1

$endgroup$

share|cite|improve this question

edited Mar 20 at 1:22

Saad

20.4k92352

asked Mar 20 at 0:54

NarimaniNarimani

1

share|cite|improve this question

edited Mar 20 at 1:22

Saad

20.4k92352

asked Mar 20 at 0:54

NarimaniNarimani

1

edited Mar 20 at 1:22

Saad

20.4k92352

edited Mar 20 at 1:22

Saad

20.4k92352

asked Mar 20 at 0:54

NarimaniNarimani

1

asked Mar 20 at 0:54

NarimaniNarimani

1