Question

Reflection property of hyperbola is applicable in which of the following
A. Radio direction finding
B. Construction of mirrors inside telescopes
C. Whispering rooms/cathedrals
D. None of these

Answer 1

Hint:If an incident ray passes through one of the focuses and strikes the convex side of the hyperbola, then the reflected ray when extended backwards passes through the other focus this is known as the reflection property of hyperbola.

Complete answer:
Every hyperbola has its own reflection property. When a light ray following the path starting from one focus falls on the hyperbola, it will reflect off 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.

As seen here in the figure:

The reflection property of hyperbola has many applications. It is used in radio direction finding (since the difference in two signals from two towers is constant along hyperbola).
Also used in construction of mirrors inside telescopes (to reflect a wide range of light coming from the hyperbolic mirror to the eyepiece).

Therefore, options A and B are correct.

Note:The reflecting property of a hyperbola will be proved for a hyperbola in standard form, with foci on the x -axis. This question was a very straightforward theoretical question, one needed to understand the concept of reflection property of hyperbola along with its graph and applications in order to solve this question.