Question

A ray emanating from the point (5, 0) is incident on the hyperbola $9x^2-16y^2=144$ at the point P with abscissa 8. Then the equation of the reflected ray if point P lies in the first quadrant is

• A. $3\sqrt{3}x-13y+15\sqrt{3}=0$
• B. $3\sqrt{3}x+13y+15\sqrt{3}=0$
• C. $3x-13\sqrt{3}y+15=0$
• D. $3x+13\sqrt{3}y-15=0$

Answer 1

The correct option is A $3\sqrt{3}x-13y+15\sqrt{3}=0$



Given hyperbola is $\frac{x^2}{16}-\frac{y^2}{9}=1$
abscissa of P is 8. Let $\alpha$ be ordinate
$(8,\alpha )$ lies on curve
$\therefore \frac{64}{16}-\frac{a^2}{9}=1\alpha =3\sqrt{3}$ ($\alpha$ in 1st quad)
$\therefore P(8,3\sqrt{3})$
$P(8,3\sqrt{3})\&S^1(-5,0)$
$\therefore Eqnisy-0=\frac{0,-3\sqrt{3}}{-5-8}(-5-8)(x+5)\Rightarrow 3\sqrt{3}x-13y+15\sqrt{3}=0$