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Question

Consider the parabola y2=4x. Let P and Q be points on the parabola where P(4,4) & Q(9,6). Let R be a point on the arc of the parabola between P and Q. Then the area of ΔPQR is largest when

A
PQR=90
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B
R(4,4)
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C
R(14,1)
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D
R(1,14)
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Solution

The correct option is C R(14,1)

Equation of PQ is
y+46+4=x494
2xy=12

Distance RL=2t22t125
Assuming
f=5RL2f=±(t2t12)=(t3)(t+2)f={(t3)(t+2) t(,2][3,)(t3)(t+2) t(2,3)

Differentiate w.r.t. t,
f=±(2t1)=0t=12
Checking for maxima and minima at t=12
f=(t3)(t+2)f=(2t1)f′′=2<0
So at t=12 it will give maxima,

Hence R=(14,1)

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