find equation in 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

i know x=rcos(theta) and y=rsin(theta) and x^2+y^2=r^2. this problem has a negative y^2 so what do i do?

i keep getting r=(2cos(theta)+10sin(theta)) / (cos(theta)^2-sin(theta)^2) but the homework program I use won't accept that as the correct answer.

Answer 1

-y² = -r² sin²(θ)

You won't be able to use r² = x² + y² for this problem.