Question

Convert the polar equation r=4sinθ to a Cartesian equation. Answer choices: x^2 + y^2 = 4y x^2 + y^2 = 4x

Answer 1

Start by multiplying both sides by r:

$r = 4 \sin \theta$
$r^2 = 4r \sin \theta$

Since $r^2 = x^2 + y^2$ and $y = r \sin \theta$, we have that

$\bf x^2 + y^2 = 4y$