Find the equation of normal to the parabola $y^{2} = 8 x$ at (8, 8) using parametric form.

2x + y = 24

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2x - y = 24

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x + y = 24

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2x + y + 24 = 0

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Solution

The correct option is A
2x + y = 24

We can see (8, 8) could be written in parametric form as form as $(2 (2)^{2}, 2 (2) (2))$ as $t = 2$ { $∵ (a t^{2}, 2 a t)$ } We know, equation of Normal to parabola at $(a t^{2}, 2 a t)$ is $y = - t x + a t^{3} + 2 a t$ . $∴$ Eqn will be y = -2x + 16 + 8.

$\Rightarrow y = - 2 x + 24$ .

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