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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 isA. `((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))` |
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Answer» Correct Answer - 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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