If the inverse point of the point (3,2) with respect to the circle x ^2+ y ^2-2 x +4 y -4=0 is (l, ~m ) then (2 l+19 ~m )=

Step-by-step solution

Given circle is x^2+y^2-2 x+4 y-4=0 Centre =(1,-2) and radius = 1+4+4 =3 We have inverse of point P( , ) w.r. to circle whose centre (h, k) and radius r is x= ( -h)+h, y= ( -k)+k, where = r^2 ( -h)^2+( -k)^2 = 9 (3-1)^2+(2+2)^2 = 9 20 Inverse point (l, m) = [ 9 20 (2)+1, 9 20 (4)-2 ]= [ 38 20 ,- 4 20 ] Now, 2 l+19 m=2 ( 38 20 )+19 ( -4 20 )=0