Assertion :If $P_{1} Q_{1}$ and $P_{2} Q_{2}$ are two focal chords of the parabola $y^{2} = 4 a x$ , then the locus of point of intersection of chords $P_{1} P_{2}$ and $Q_{1} Q_{2}$ is directrix of the parabola. Here $P_{1} P_{2}$ and $Q_{1} Q_{2}$ are not parallel Reason: The locus of point of intersection of perpendicular tangents of parabola is directrix of parabola

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Let $P_{1} (a t_{1}^{2}, 2 a t_{1})$ & $Q_{1} (\frac{a}{t_{1}^{2}}, \frac{- 2 a}{t_{1}})$
$P_{2} (a t_{2}^{2}, 2 a t_{2})$ & $Q_{2} (\frac{a}{t_{2}^{2}}, \frac{- 2 a}{t_{2}})$
on $y^{2} = 4 a x$
equation of $P_{1} P_{2}$ :
$(t_{1} + t_{2}) y = 2 x + 2 a t_{1} t_{2}$ .......(i)
equation of $Q_{1} Q_{2}$
$- (t_{1} + t_{2}) y = 2 x t_{1} t_{2} + 2 a$ ......(ii)
add (i) & (ii)
$x = - a$
which is directerix of $y^{2} = 4 a x$
Locus of point of intersection of tangent is directrix, in case of parabola

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