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Let a,r,s,t be non-zero real numbers. Let P `(at^(2), 2at),Q R(ar^(2), 2ar)` and S `(as^(2), 2as)` be distinct point on the parabola `y^(2) = 4ax`. Suppose the PQ si the focal chord and line QR and PK are parallel, where K is point (2a, 0) It 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 Plan Equation of tangent and normal at `(at^(2), 2at)` are given by `ty = x + at^(2)` and `y + tx = 2a + at^(3)`, respectively. Tangent at `P + ty = x + at^(2)` or `y = (x)/(t) + at` Normal at `S : y (x)/(t) = (2a)/(t) + (a)/(t^(3))` Solving `2y = at + (2a)/(t) + (a)/(t^(3)) implies y = (a(t^(3) + 1)^(2))/(2t^(3))` |
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