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Definition of Functions

If the equati...

Question

If the equation of normal to the ellipse $4 x^{2} + 9 y^{2} = 36$ at the point $(3, - 2)$ is $p x + q y = r$ . Find the value of $p + q + r .$

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Solution

The correct option is C $10$
Equation of normal is $\frac{a^{2} x}{x_{1}} - \frac{b^{2} y}{y_{1}} = a^{2} - b^{2}$
$\Rightarrow \frac{9 x}{3} - \frac{4 y}{- 2} = 5$
$\Rightarrow 3 x + 2 y = 5$
Therefore, $p + q + r = 10$

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