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f(x) Transforms to f(-x)

If curves x...

Question

If curves $x^{2} = 9 a (9 - y)$ and $x^{2} = a (y + 1)$ intersect orthogonally then value of $a$ is

A

1

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B

2

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C

3

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D

4

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Solution

The correct option is C $4$
For $x^{2} = 9 a (9 - y); \frac{d y}{d x} = \frac{- 2 x}{9 a} = m_{1}$
For $x^{2} = a (y + 1); \frac{d y}{d x} = \frac{2 x}{a} = m_{2}$
$m_{1} m_{2} = - 1$ gives $4 x^{2} = 9 a^{2} . . . . (1)$
also by eliminating $y$ between the equation of curves $x^{2} = 9 a . . . . . (2)$
From (1) and (2) we get $a = 4$

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