Let P and Q be the inverse points with respect to the circle S x^2+y^2-4 x-6 y+k=0 and C be the centre of the circle S=0 such that C P . C Q=4 . If P=(1,2) and Q =( a , b ) , then 2 a =

Step-by-step solution

We have C P C Q=r^2=4 r=2 Centre of given circle x^2+y^2-4 x-6 y+k=0=C(2,3) . We know that inverse of point P( , ) with respect to circle with centre (h, k) and radius r is the point (a, b) then a= ( -h)+h and b= ( -k)+k aligned & where = r^2 ( -h)^2+( -k)^2 & = 4 (1-2)^2+(2-3)^2 =2 & a=2(1-2)+2=-2+2=0 . aligned