Show by calculation that the point \(P(-9,-3)\) lies inside the circle \[x^2+y^2+4x-8y-80=0.\]

Can we find the centre and the radius of the circle? How far is \(P\) from the centre of the circle?

Find the equations of the two circles which pass through \(P\), touch the given circle, and have radii of 5 units.

We know these circles pass through \(P\) — can we find another point that these circles must go through?