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

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Solution

The correct option is B 9
A normal to the parabola $y^{2} = 4 a x$ has the equation $y = m x - 2 a m - a m^{3}$
Comparing this equation with the given equation $x + y = k,$
we get $m = - 1$ and we know a to be $3$ .
So, the equation becomes $y + x = 6 + 3 = 9$
$\Rightarrow k = 9$

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