# Show that the circles touch externally and find the coordinate where thy touch

I have 2 equations:

${x^2 + y^2 - 10x - 12y + 36 = 0}$

${x^2 + y^2 + 8x + 12y - 48 = 0}$

From this, the centre and radius of each circle is

(5, 6) and a radius of 5 (-4, -6) and a radius of 10

In order to prove that the circles touch externally the distance between the 2 centres is the same of the sum of the 2 radii or 15.

Using the distance formula I get

${{\sqrt {(-4 - 5)^2 + (-6 - 6)^2}}}$

Which is ${\sqrt {81 + 36} = \sqrt 225 = 15}$

So they touch externally but how can if I find the point where they intersect?

• sorry, I had a typo in the first equation. – dagda1 Sep 21 '15 at 20:34