Locating a Moving Point P: x+y=9

[Michael_Light]

Homework Statement

A moving point P is such that the length of the tangent from P to the circle x²+y²=16 is equal to the distance of P from point (8,8). Show that the locus of P is the straight line x+y=9.

Homework Equations

The Attempt at a Solution

I sketched a graph for this, but it doesn't seems to help me a lot in solving this question. Can anyone give me some hints? Thanks...

 

[praharmitra]

Well, let the point P be (a,b). What is the length of the tangent to the circle? What is its distance from (8,8)? Equate the two.