Question

Which of the following is true about reflection property of hyperbola?

• A. A ray directed towards one focus will reflect off of the hyperbola towards the other focus.
• B. If a ray of light emerges from one focus and is reflected from either branch of the hyperbola, the light-ray appears to have come from the other focus.
• C. By reversing the direction of the light, rays directed at one of the foci are reflected towards the other focus.
• D. None of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A If a ray of light emerges from one focus and is reflected from either branch of the hyperbola, the light-ray appears to have come from the other focus.
B A ray directed towards one focus will reflect off of the hyperbola towards the other focus.
C By reversing the direction of the light, rays directed at one of the foci are reflected towards the other focus.

We know that for a hyperbola there are two points of focus,. For any hyperbola with origin at $(0,0)$ and coordinate axes as major and minor axes, the two foci lie at $(ae,0)$ and $(-ae,0)$ respectively.

Every hyperbola has it's own reflection property.

When a light ray following the path starting from one focus falls on Hyperbola, it will reflect off of the hyperbola directly away from the other focus.

Similarly, if a ray directed towards one focus will reflect off of the hyperbola towards the other focus.

Hence we can see option $A$,$B$ and $C$. all of them are correct.