1.

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 is

Answer»

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

SOLUTION :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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