Assertion :If normal at the ends of double ordinate $x = 4$ of parabola $y^{2} = 4 x$ meet the curve again at $P$ and $P^{'}$ respectively, then $P P^{'} = 12$ unit Reason: If normal at $t_{1}$ of $y^{2} = 4 a x$ meets the parabola again at $t_{2}$ , then $t_{1}^{2} = 2 + t_{1} t_{2}$

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 C Assertion is correct but Reason is incorrect
End point of double ordinate $x = 4$ of $y^{2} = 4 x$ are $(4, \pm 4)$
$\Rightarrow t_{1} = \pm 2$
$\Rightarrow t_{2} = - t_{1} - \frac{2}{t_{1}} = \pm 3$
$\Rightarrow P (9, 0)$ and $P^{'} (9, - 6)$
$∴ P P^{'} = 12$

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Assertion :If normal at the ends of double ordinate x=4 of parabola y2=4x meet the curve again at P and P′ respectively, then PP′=12 unit Reason: If normal at t1 of y2=4ax meets the parabola again at t2, then t21=2+t1t2

The correct option is C Assertion is correct but Reason is incorrectEnd point of double ordinate x=4 of y2=4x are (4,±4)⇒t1=±2⇒t2=−t1−2t1=±3⇒P(9,0) and P′(9,−6)∴PP′=12

Assertion :If normal at the ends of double ordinate $x = 4$ of parabola $y^{2} = 4 x$ meet the curve again at $P$ and $P^{'}$ respectively, then $P P^{'} = 12$ unit Reason: If normal at $t_{1}$ of $y^{2} = 4 a x$ meets the parabola again at $t_{2}$ , then $t_{1}^{2} = 2 + t_{1} t_{2}$

The correct option is C Assertion is correct but Reason is incorrect
End point of double ordinate $x = 4$ of $y^{2} = 4 x$ are $(4, \pm 4)$
$\Rightarrow t_{1} = \pm 2$
$\Rightarrow t_{2} = - t_{1} - \frac{2}{t_{1}} = \pm 3$
$\Rightarrow P (9, 0)$ and $P^{'} (9, - 6)$
$∴ P P^{'} = 12$