If x + y = k is normal to y 2 = 12 x , then k is [2000]

Question

If $x + y = k$ is normal to $y^{2} = 12 x$ , then $k$ is [2000]

Smart Achievers · Accepted Answer

(2)

$y = m x + c$ is normal to the parabola $y^{2} = 4 a x$ if $c = - 2 a m - a m^{3}$

Now given line $x + y = k$ is normal to $y^{2} = 12 x$

$∴$ $m = - 1, c = k and a = 3$

$\Rightarrow c = k = - 2 (3) (- 1) - 3 {(- 1)}^{3} = 9$

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