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The slopes of the normals to the parabola $y^{2} = 4 a x$ intersecting at a point on the axis of the parabola at a distance 4a from its vertex are is

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answer is C.

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Detailed Solution

$y = m x - 2 a m - a m^{3}$

Passing $(4 a, 0) \Rightarrow m = 0, \pm \sqrt{2}; - \sqrt{2}, 0, \sqrt{2}$ an in AP

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