Equation of the normal at a point on the parabola $y^{2} = 36 x$ whose ordinate is three times its abscissa is

2 x + 3 y + 44 = 0

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2 x - 3 y + 44 = 0

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2 x + 3 y - 44 = 0

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2 x - 3 y = 0

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Solution

The correct option is D $2 x + 3 y - 44 = 0$
Equation of the normal at the point $({9 m}^{2}, - 18 m)$
$($ For $a = 9)$ to the parabola $y^{2} = 4 \times 9 x$ is
$y = m x - 2 \times 9 m - {9 m}^{3}$ where
$- 18 m = 3 ({9 m}^{2})$ $\Rightarrow m = - \frac{2}{3}$ or $0$
neglecting $m = 0$
For $m = - \frac{2}{3}$ , the normal is $2 x + 3 y - 44 = 0$

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