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Let $Q$ be the foot of the perpendicular from the
origin $O$ to the tangent at a point $p (α, β)$ on the
parabola $y^{2} = 4 a x,$ and $S$ be the focus of the parabola,
then $(O Q)^{2} (S P)$ is equal to

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detailed solution

Correct option is B

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Let $Q$ be the foot of the perpendicular from the
origin $O$ to the tangent at a point $p (α, β)$ on the
parabola $y^{2} = 4 a x,$ and $S$ be the focus of the parabola,
then $(O Q)^{2} (S P)$ is equal to