The line y = 2x + k is a normal to the parabola $y^{2} = 4 x$ then k =

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-12

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-10

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Solution

The correct option is B -12
$y = 2 x + k \Rightarrow 2 x - y + k = 0. H e r e l = 2, m = - 1, n = k a n d a = 1$
$y = 2 x + k i s a n o r m a l t o y^{2} = 4 x \Rightarrow a l^{2} + 2 a l m^{2} + m^{2} n = 0$
$\Rightarrow 1 (2)^{3} + 2 (1) (2) (- 1)^{2} + k = 0 \Rightarrow k + 12 = 0 \Rightarrow k = - 12$

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