Review question

# Can we find the equations of two circles that touch another? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5624

## Suggestion

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?