A tangent at a point on the circle x2+y2=a2 intersect a concentric circle S at P and Q. The tangents of this circle at, P,Q meet on the circle x2+y2=b2. The equation of the concentric circle S is
Take, any point on x2+y2=b2 as P(bcosθ,bsinθ)
From P (bcosθ,bsinθ) take
a chord of contact of circle S.
This chord of contact is tangent to x2+y2=a2
Chord of contact to circle S: x2+y2=r2
is
xx1+yy1−r2=0
xbcosθ+ybsinθ−r2=0
∴ distance of (0,0) to $xbcos\theta+b
sin \theta y-r^{2}=0$ is a.
|r2√b2|=a
r2=ab.
∴r=√ab
∴ equation of circle S is
x2+y2=r2
→x2+y2=ab