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Q.

Let Q be the foot of the perpendicular from theorigin O to the tangent at a point p(α,β) on the parabola y2=4ax, and Sbe the focus of the parabola,then (OQ)2(SP) is equal to

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a

α

b

aα2

c

β

d

aβ2

answer is B.

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Detailed Solution

Let α=at2,β=2atEquation of the tangent at P(α,β) is ty=x+at2⇒OQ=at21+t2SP=at2+1 So (OQ)2(SP)=a2t41+t2×a1+t2=a3t4=aα2

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Let Q be the foot of the perpendicular from theorigin O to the tangent at a point p(α,β) on the parabola y2=4ax, and Sbe the focus of the parabola,then (OQ)2(SP) is equal to