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The point $P (α, β), β > 0$ is a point of intersection of the curves $C_{1}, C_{2}$ whose equations are $y^{2} = 24 x a n d \frac{x^{2}}{100} + \frac{y^{2}}{225} = 1$ respectively. The normal to the curve $C_{1}$ at the point P passes through the point

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$(- 11, 4)$

$(\frac{- 7}{3}, \frac{61}{3})$

$(\frac{- 15}{2}, \frac{1}{2})$

$(2, - 3)$

answer is B.

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Detailed Solution

Point of intersection of the given curves is (6, 12)
$∴$ Equation of the normal at P(6, 12) to $y^{2} = 24 x$ is
$x + y - 18 = 0$

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