Question

The normal to the hyperbola `x^2/a^2 - y^2/9` = 1 at the point `(8, 3sqrt(3))` on it passes through the point ______.

Options

• `(15, -2sqrt(3))`

• `(9, 2sqrt(3))`

• `(-1, 9sqrt(3))`

• `(-1, 6sqrt(3))`

Answer 1

The normal to the hyperbola `x^2/a^2 - y^2/9` = 1 at the point `(8, 3sqrt(3))` on it passes through the point `underlinebb((-1, 9sqrt(3))`.

Explanation:

Given hyperbola is `x^2/a^2 - y^2/9` = 1

∵ `(8, 3sqrt(3))` lie on hyperbola then point will satisfy it

`\implies 64/a^2 - 27/9` = 1

`\implies a^2 = 64/4` = 16

Now, equation of normal at `(8, 3sqrt(3))` :

`(16x)/8 + (9y)/(3sqrt(3))` = 16 + 9

`2x + sqrt(3)y` = 25

On putting x, y from the given options, we get option (c) is correct.