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Q.

PN is an ordinate of the parabola y2=4ax (P on y2=4ax and N on  x-axis). A straight line is drawn parallel to the axis to bisect NP and meets the curve in QNQ  meets the tangent at the vertex A in a point T such that AT=k·NP, then the value of k is (where A is the vertex)

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a

23

b

1

c

32

d

13

answer is B.

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Detailed Solution

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Consider the figure

Question Image

 

 

 

Observing the above graphAT=4at3.NP=2at

Therefore, k=23

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PN is an ordinate of the parabola y2=4ax (P on y2=4ax and N on  x-axis). A straight line is drawn parallel to the axis to bisect NP and meets the curve in Q. NQ  meets the tangent at the vertex A in a point T such that AT=k·NP, then the value of k is (where A is the vertex)