How to convert 𝑦^2=3−𝑥^2 from rectangular form to polar form?

Answer 1

Hi Rose:

Here's how to do this type of question. The important equations are x = r cos θ and y = r sin θ ........ eqn (1)

The rectangular equation is x² + y² = 3 [we know this is a circle, center the origin and radius √3

Substituting for x and y from eqn (1): (r cos θ)² + (r sin θ)² = 3

r² cos²θ + r²sin²θ = 3

r²(sin²θ + cos²θ) = 3

r² = 3 [since sin²θ + cos²θ = 1 for any angle θ

r = √3

which is the polar equation for a circle, center the origin and radius √3