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Let a, r, s, t be non-zero real numbers....

Let a, r, s, t be non-zero real numbers. Let `P(at^(2),2at),Q(ar^(2),2ar)andS(as^(2),2as)` be distinct points on the parabola `y^(2)=4ax`. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K the point (2a,0).
If st=1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

A

`((t^(2)+1)^(2))/(2t^(3))`

B

`(a(t^(2)+1)^(2))/(2t^(3))`

C

`(a(t^(2)+1)^(2))/(t^(3))`

D

`(a(t^(2)+2)^(2))/(t^(3))`

Text Solution

Verified by Experts

The correct Answer is:
B
2 Tangent at `P:ty=x+at^(2)ory=(x)/(t)+at`
Normal at `S:y+(x)/(t)=(2a)/(t)+(a)/(t^(3))`
Solving, `2y=at+(2a)/(t)+(a)/(t^(3))`
`rArry=(a(t^(2)+1)^(2))/(2t^(3))`
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