Point M moved on the circle (x−4)2+(y−8)2=20.Then it broke away from it and moving along a tangent to the circle cut the x-axis at point (-2,0). The coordinates of the point on the circle at which the moving point broke away is

x2+y2−8x−16y+60=0 -----(i)  Equation of chord of contact from (−2,0) is  −2x−4(x−2)−8y+60=0 or 3x+4y−34=0------(ii) Solving (i) and (ii), we get x2+34−3x42−8x−1634−3x4+60=0  or  16x2+1156−204x+9x2−128x−2176+192x+960=0  or 5x2−28x−12=0 or (x−6)(5x+2)=0 or x=6,−25  Therefore, the points are (6,4) and (−2/5,44/5).