Question

Convert the rectangular equation x ^ 2 + y ^2 = 2 y to polar form

Answer 1

Explanation:

The main equivalence between rectangular and polar forms is

x^2 + y^2 = r^2, where r is the radius. Next, y = r sin Ф. Thus,

x^2 + y^2 = r^2 becomes r² = 2·r·sin Ф.

The variable r can be factored out partially: r = 2·sin Ф

This is the polar form of x^2 + y^2 = 2y.