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Question

If the tangent at the point P(2, 4) to the parabola y2=8x meets the parabola y2=8x+5 at Q and R,
then the midpoint of QR is


A

(2, 4)

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B

(4, 2)

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C

(7, 9)

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D

(3, 3)

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Solution

The correct option is A

(2, 4)


For the parabola y2=8x, the point P(2, 4) corresponds to t =1.
slope of targent at at2,2at is 1t
Hence the tangent to the parabola y2=8x at (2, 4) is
y4=11(x2)xy+2=0y=x+2y=x+2 intersects the parabola y2=8x+5(x+2)2=8x+5x2+4x+4=8x+5x24x1=0Solving for x,x=4 ± 1642=4 ± 232=2±3
corresponding y coordinates are
x+24±3Q=(2+3,4+3)R=(23,43)
The midpoint of QR =(2, 4)


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