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If the normals at two points $P$ and $Q$ on the parabola $y^{2} = 4 x$ , meet on the parabola, then the locus of the point of intersection of the tangents at $P$ and $Q$

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Can be a straight line parallel to the axis of the parabola

Can be the curve y² (x + 2) + 4 = 0

Can be the curve y² (x + 2) - 4 = 0

Can be straight line parallel to the directrix of the parabola

answer is B, C.

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Detailed Solution

Let P(t₁) Q(t₂) case -1 $t_{1} + t_{2} = - \frac{2}{t_{1}}$
So focus is y²(x + 2) + 4 = 0 case - II t₁t₂ = 2 So focus is x = 2

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