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Question

Consider a parabola y2=4x, Let A be the vertex of parabola, P be any point on the parabola and B is a point on the axis of parabola, if PAPB, then the locus of centroid of PAB is

A
9y2=6x8
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B
9y2=6x+8
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C
9y2=6x8
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D
9y2=6x+8
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Solution

The correct option is C 9y2=6x8
Here, A(0,0) P(at2,2at)
Slope of AP=2at0at20=2t
Equation of BP is y2t=t2(xt2)
for coordinates of B, put y=0 in above equation
02t=t2(xt2)
x=t2+4
B(t2+4,0)
Centroid G=(0+at2+t2+43,0+2at+03)G=(0+t2+t2+43,0+2t+03) (a=1)3x=2t2+4,3y=2t3x=2(3y2)2+49y2=6x8

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