polar coordinates?

Question

how would i find an equation in polar coordinates if i am given the cartesian equation (x-1)^2-(y+5)^2=-24

Answer 1

x = r cos(θ)
y = r sin(θ)

Substitute these into the Cartesian equation and expand the result. You will get a quadratic equation for r, but you will find that the constant term drops out. Assuming you have it in a form such that the right side is zero, factor out an r from the left side, and so r=0, or the other term (which is linear in r) is zero. You will find that the result of solving the linear-in-r term for r includes the case where r=0 (for θ = π/4, for example) so you can ignore the explicit "r=0" solution (which is just the Cartesian point (0,0)).