Question

How do you convert `r = 50 sinθ` to rectangular form?

Answer 1

`x^2+y^2-50y=0`

Explanation:

At other than pole r = 0, mulyiply both sides by r and use `r^2=x^2+y^2 and y = r sin theta`.
So, `x^2+y^2-50y=0`.

This represents the circle through the origin r = 0. The center is at (0, 25) and the radius is 25.

In polar form, `r = 2a sin theta and r = 2a cos theta` represent families of circles through the origin, with centers on either axis. a is the parameter (giving size) for the members of the families.

These are degenerate cases of rose curves (with petals) through the origin, given by `r = 2a sin ntheta and r = 2a cos ntheta`.