If $x + y = k$ is a normal to the parabola $y^{2} = 12 x$ then $k$ is

3

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9

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Solution

The correct option is B $9$
Equation of normal to the parabola $y^{2} = 4 a x$ is given by
$y = m x - 2 a m - a m^{3} . . (1)$ , (Here $a = 3)$
Now since line (1) and $y = - x + k$ represent same line
$\Rightarrow m = - 1 ∴ k = - 2 a m - a m^{3} = - 2 (3) (- 1) + 3 (1) = 9$

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