Find the equation of the circles passing through (-4,3) and touching the lines x+y=2 and x-y=2.

Expalnation

The two lines are perpendicular to each other and are also tangents of the circle. So the intersection point of these two lines lies on the director circle whose radius is 2^0.5R so assuming the centre of the circle to be h,k and using the general equation of the circle and putting co-ordinates (-4,3) in the equation and putting co-ordinates (2,0) in the director circle's general equation and solving it terms of h,k to get the equation of the circle i.e.

                                                                                     (x-6)2 + (y-6)2 = 26