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Equation of Normal at Given Point

If the normal...

Question

If the normal at point $(1, 2)$ on the parabola $y^{2} = 4 x$ meets the parabola again a point $(t^{2}, 2 t),$ then the value of $t$ is

1

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Solution

The correct option is D $- 3$
If the normal at point $P (t_{1}) = (a t_{1}^{2}, 2 a t_{1})$ on the parabola $y^{2} = 4 a x$ meets the parabola again a point $Q (t) = (a t^{2}, 2 a t),$ then
$t = - t_{1} - \frac{2}{t_{1}}$
For $y^{2} = 4 x \Rightarrow a = 1$
$P = (1, 2) \Rightarrow t_{1} = 1 ∴ t = - 1 - 2 = - 3$

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