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Question

If normal at p to parabola y2=4ax meets parabola again at Q such that PQ subtends a right angle at the vertex of y2=4ax then p will be



Your Answer
A

Your Answer
B

Correct Answer
C

Your Answer
D


Solution

The correct option is B


It is useful to remember that fact that,If normal at

(at21,2at1) meet the parabola at (at22,2at2) then,

t2=t12t1     .........(1)

Here, Given slope of PO=2at1at21=2t1

Slope of QO=2at2at22=2t2

And (slope of PO)(slope of QO)=-1

(2t1)(2t2)=1t1t2=4    ......(2)

From (1),t2=t12t1

From (2),t2=4t1

4t1=t1+2t1

4=t21+2

t1=±2

p=(2at,at2)=(2a(±2),a(2))

                         =(±22a,2a)

Only option c satisfies.

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