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Question

Let P(4,4) and Q(9,6) be two points on the parabola y2=4x and let X be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of PXQ is maximum. Then 4 times this maximum area (in sq. units) is

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Solution

Cosider the parabola y2=4x
Let the coordinates of point X is (t2,2t)


Area of PXQ
=12[t2(46)2t(49)+1(24+36)]
=12[10t2+10t+60]
=5(t2+t+6)
=5[254(t12)2]
Hence area will be maximum when t=12
maximum area =5(254)
=1254sq. units

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