Write the rectangular equation in polar form.

Question

Write the rectangular equation x2 + y2 = 9 in polar form.

 

What will r equal?

Answer 1

Here the trick to answer this question, 

you have the formal equation which is  x2 + y2 = r2

and we have                                           x2 + y2 = 9 

If we compare the both equations we will realize that r2=9⇒ r=3    that simple!!!

Answer 2

Hi Chyna,

 

In polar coordinates, x = r cos (theta), y = r sin(theta)

 

This is an equation (x^2 + y^2 = 9) of a circle with a radius of 3.

 

So in polar coordinates it would by

 

[r cos(theta) ]^2  +  [ r sin(theta) ]^2 = 9

 

r^2 [cos(theta)]^2  + r^2 [sin(theta)]^2 = 9

 

Factor out "r^2"

 

r^2 [(cos(theta))^2 + (sin(theta))^2] = 9

 

Since cos^2 + sin^2 = 1, this becomes

 

r^2 (1) = 9

 

r = sqrt(9)

 

In polar form this equation would be

 

 

r = 3