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Question

A tangent is drawn to the parabola y2=4x at a point P on the parabola in the first quadrant and another tangent is drawn to the vertex A of the parabola. Let both the tangent meet at a point B,if area of the triangle ABP=32 unit2, then equation of the tangent is

A
4y=x+8
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B
2y=x+8
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C
4y=x+16
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D
4x=y+16
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Solution

The correct option is C 4y=x+16
Let the coordinates of P(t2,2t)
For the given parabola tangent at vertex will be yaxis
equation of the tangent to the parabola at P will be
yt=x+t2
for the coordinates of B; x=0
y=tB(0,t)

So the required area will be
t2t2=32t3=26t=4
So the equation of the tangent will be
4y=x+16

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