Question

How do you find the cartesian equation for `r = 4 + 4cosT`?

Answer 1

The cartesian equation for this cardioid is
x.x + y.y = 4 `sqrt`(x.x + y.y) + 4x.

Explanation:

r = `sqrt`(x.x + y.y) and x = r cos T. Multiply both sided by r.
Rationalization to remove `sqrt` would give a 4th degree equation.
This equation would include r = `-`4 + 4 cos T, also representing the same graph, drawn from r = 0 and T = 0, instead of from ( 8, 0 ). Negative r locates the point in the opposite direction.
Here, T = `pi` gives r = `-`8 which is ( 9, 0 ) for the given equation. .