locus problem (s.5)

Two concentric circles x^2+y^2=9 and x^2+y^2=25 are given. A variable point P moves in such a way that it is equidistant from the two circles. Find the equation of the locus of P.
不要只比答案 要詳細做法
as you can see,
the locus of point P should be a circle and it is also the concentric circles of the given two equations.P lies on the middle of these two lines
now,the centre of these equations are:(0,0)
so,let point P is (x,y),r is the radius of P
(x - 0)^2 + (y - 0)^2 = r^2
x^2 + y^2 = r^2
since it is on the middle,
the radius of two circle is 3 and 5 respectively,
so,
r = (3 + 5) /2
r = 4
Hence,the required locus is
x^2 + y^2 = 16
圖片參考：http://hk.yimg.com/i/icon/16/1.gif

Radius of circle 1 = 3
Radius of circle 2 = 5
Let P(x, y) be the point on locus
Distance of P from origin = sqrt (x^2+y^2)
Then,
sqrt (x^2+y^2) - 3 = 5 - sqrt (x^2+y^2)
2 * sqrt (x^2+y^2) = 8
sqrt (x^2+y^2) = 4
x^2+y^2 = 16