The pole of a straight line with respect to the circle x2+y2=a2 lies on the circle x2+y2=9a2 If the straight line touches the circle x2+y2=r2 thena2r2 is equal to

Let (α,β) be the pole of the given straight line with respect to the circle x2+y2=a2 Then, the equation of the polar isαx+βy−a2=0It is given that (α,β) lies on the circle x2+y2=a2∴ α2+β2=9a2Since line in (i) touches the circle x2+y2=r2∴−a2α2+β2=r⇒a29a2=r⇒9r2=a2