Let a circle C of radius 5 lie below the x -axis. The line L 1 = 4 x + 3 y + 2 passes through the centre P of the circle C and intersects the line L 2 : 3 x - 4 y - 11 = 0 at Q . The line L 2 touches C at the point Q . Then the distance of P from the line 5 x - 12 y + 51 = 0 is

Step-by-step solution

Plotting the diagram of given data, we get Finding intersection point of 4 x + 3 y + 2 = 0 and 3 x - 4 y - 11 = 0 we get 1 , - 2 Now finding the point P by parametric we get, x - 1 cos θ = y + 2 sin θ = ± 5 y = - 2 + 5 - 4 5 = - 6 x = 1 + 5 3 5 = 4 Now finding distance of point P from line 5 x - 12 y + 51 = 0 = 5 4 - 12 - 6 + 51 13 = 20 + 72 + 51 13 = 143 13 = 11