Question

The normal to the hyperbola
$\frac{x²}{a²} - \frac{y²}{9} = 1$
at the point (8, 3√3) on it passes through the point:

• A. $(15, -2\sqrt3)$
• B. $(9, 2\sqrt3)$
• C. $( -1, 9\sqrt3)$
• D. $( -1, 6\sqrt3)$

Answer 1

Answer: (C)

$( -1, 9\sqrt3)$

Answer 2

The correct answer is (C) : $(-1,9\sqrt3)$
Given hyperbola :
$\frac{x²}{a²} - \frac{y²}{9} = 1$
∵ It passes through
$(8, 3\sqrt3)$
$∵ \frac{64}{a²} - \frac{27}{9} = 1 ⇒ a² = 16$
Now , equation of normal to hyperbola
$\frac{16x}{8} + \frac{9y}{3\sqrt3} = 16 + 9$
$⇒ 2x + \sqrt3y = 25 ...... (i)$
$(-1 , 9\sqrt3)$ satisfies (i)