Convert the Cartesian equation to the polar equation

[Fatima Hasan]

Homework Statement

Replace the Cartesian equation with an equivalent polar equation.
$x^2 + (y - 18)^2 = 324$
a)$r = 36 sin θ$
b)$r^2 = 36 cos θ$
c)$r = 18 sin θ$
d)$r = 36 cos θ$

Homework Equations

$x= r cos \theta$
$y= r sin \theta$
$x^2 + y^2 = r^2$

The Attempt at a Solution

$x^2 + (y - 18)^2 = 324$
$x^2 + y^2 - 2*18*y + 18^2 = 324$
$x^2 + y^2 - 36 y =0$
$r^2 = 36 y$
Divide by r :
$r = 36 r sin \theta$
So , the answer is (a) .Right ?

 

[stevendaryl]

Your derivation looks right to me.