The normal to the hyperbola ( x 2/ a 2)-( y 2/9)=1 at the point (8,3 √3) on it passes through the point :

Question

The normal to the hyperbola ( x 2/ a 2)-( y 2/9)=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)

Tardigrade Admin · Accepted Answer

(x2/a2)-(y2/9)=1 .(8,3 √3) lie on Hyperbola then (64/a2)-(27/9)=1 ⇒ a2=(64/4)=16 equation of normal at (8,3 √3): (16 x/8)+(9 y/3 √3)=16+9 2 x+√3 y=25

Q. The normal to the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{9} = 1$ at the point $(8, 33)$ on it passes through the point :

$(15, - 23)$

$(9, 23)$

$(- 1, 93)$

$(- 1, 63)$

$\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{9} = 1. (8, 33)$ lie on Hyperbola then $\frac{64}{a ^{2}} - \frac{27}{9} = 1$
$\Rightarrow a^{2} = \frac{64}{4} = 16$
equation of normal at $(8, 33)$ :
$\frac{16 x}{8} + \frac{9 y}{3 3} = 16 + 9$
$2 x + 3 y = 25$

Q. The normal to the hyperbola a2x2​−9y2​=1 at the point (8,33​) on it passes through the point :

(15,−23​)

(9,23​)

(−1,93​)

(−1,63​)