Question

How do you convert `8=(4x-11y)^2+3y` into polar form?

Answer 1

Substitute `x = rcos(theta) and y = rsin(theta)`.

Explanation:

Given `x = rcos(theta) and y = rsin(theta)`, we have
`8 = (4rcostheta - 11rsintheta)^2 + 3rsintheta`

`8 = (r[4costheta - 11sintheta])^2 + 3rsintheta`

`8 = r^2(4costheta - 11sintheta)^2 + 3rsintheta`

We can use FOIL to simplify the expression in parentheses, but it doesn't lead us anywhere "nice."

We could solve for r using the Quadratic Formula if we are required to, but this is positively unfriendly, and the equation is already in a Polar form.