Question

How do you convert `3y= 12x-12` into a polar equation?

Answer 1

r = `-`1 / ( sin `theta` `-` 4 cos `theta` ). Represents a straight line through polar ( 1, 3`pi`/2), with inclination arc tan 4 to `theta` = 0.

Explanation:

y = m x + c in polar form is r = c / ( sin `theta` `-` m cos `theta` ).
Note that ( r, `theta` ) is same as (`-` r, `theta` + `pi` ).