Find the equation of normal having slope 1 to the parabola
$y^{2} = 4 x$

$y = x - 3$

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$y = x + 3$

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$y = x$

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$y = 2 x - 3$

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Solution

The correct option is A
$y = x - 3$

For a given slope m the equation of unique normal is given by $y = m x - 2 a m - a m^{3}$

Here a = 1.

$y = (1) x - 2 (1) (1) - (1) (1)^{3} y = x - 2 - 1 y = x - 3$

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Given slope m, find the equation of normal having slope m to the parabola $y^{2} = 4 a x$

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Given slope m, find the equation of normal having slope m to the parabola $y^{2} = 4 a x$

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