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 PA⊥PB, then the locus of centroid of △PAB is
A
9y2=−6x−8
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B
9y2=6x+8
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C
9y2=6x−8
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D
9y2=−6x+8
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Solution
The correct option is C9y2=6x−8 Here, A(0,0)P≡(at2,2at)
Slope of AP=2at−0at2−0=2t ⇒ Equation of BP is y−2t=−t2(x−t2)
for coordinates of B, put y=0 in above equation ∴0−2t=−t2(x−t2) ⇒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=2t⇒3x=2(3y2)2+4∴9y2=6x−8