Question

Rewrite the rectangular equation x^2+y^2-8y=0 as a polar equation

Answer 1

We'll use the following identities:

r = √(x2 + y2), from which we also have r2 = x2 + y2

y = r*sinθ

First, let's re-write your equation:

r = 8*sin(θ). Multiply both sides by r:

r2 = 8r sin(θ)

Now, we'll use substitute using the identities:

x2 + y2 = 8y

Re-arrange and complete the square:

x2 + y2 - 8y = 0

x2 + (y-4)2 - 16 = 0

x2 + (y-4)2 = 16

This represents a circle with center (0,4), and radius 4.

Explanation:

sorry if it wrong