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Question

The coordinates of the point of contact of the tangent to the parabola y2=16x, which is perpendicular to the line 2xy+5=0 are


  1. (16, 16)

  2. (16, -16)

  3. (1, 4)

  4. (1, -4)


Solution

The correct option is B

(16, -16)


y2=16x          .........(1)4a=16a=42xy+5=0   .......(2)
A line is perpendicular to the line (2) is
x+2y+λ=0      ......(3)Slope, m=12
Slope of the tangent to a parabola at (at2,2at) is 1t. Hence, a line having slope m intersects the parabola at (am2,2am)
Line (3) touches the parabola (1). So, the coordinates of the point of contact is
P(am2,2am)=(16,16)

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