The point on the straight line y=2x+11 which is nearest to the circle 16 x2+y2+32x−8y−50=0, is

Clearly, required point is the point of intersection of the line y=2x+11and the line perpendicular to it passing through the centre of the circle.The coordinates of the centre are (−1,1/4)The equation of the line through(-1, 1 / 4) and perpendicular to y=2x+11 isy−14=−12(x+1)⇒2x+4y+1=0Clearly, (- 9/2, 2) is the point of intersection of y = 2x + 11 and 2x+4y+1=0.So, the coordinates of the required point are (- 9 / 2 , 2)