Question

The normal to the hyperbola x²/a² + y²/9 = 1 at the point (8, 3√3) on it passes through the point:

(A) (15, -2√3)

(B) (9, 2√3)

(C) (-1, 9√3)

(D) (-1,6√3)

Answer 1

Correct option is (C)(-1, 9√3)

\(\frac{x^2}{a^2}=1:(8, 3\sqrt3)\) lie on hyperbola then

\(\frac{64}{a^2}-\frac{27}9=1 \)
⇒ a² = 64/4 = 16

equation of normal at (8, 3√3):