## March 29, 2009

### Elliptical carrom board

Slightly different kind of a question.

Say you construct an elliptical carrom board and keep the striker on a focus point (see the diagram below) and strike it. Which point on the board is the striker surely going to pass through after rebound irrespective of the angle at which it was struck?

Also, tell us which property of the ellipse lets you arrive at this.

p.s: Although it looks like a math question, it is very much quiz style.

Cracked by:Â Shrey Goyal , udupendra , Dibyo , Raghuvansh , u2001137 , Jean Valjean , Anand Shankar , Ps , sidsen , Rohan , madhur , Nakul , Krishna , yaksha , duriel , Neeraj , Poornima , Ananth , shrik , sand , p vs np , MGS and Ajay Parasuram.

Answer:

The striker will pass through the other focus.

p vs np has a crisp explaination of the reason

“This is so, because the normal at the point of intersection of the lines passing through the two focii on the perimeter of the curve, is the angular bisector of the angle formed. Hence, by rules of ideal reflectivity (incidence angle= reflected angle), it needs to pass through the other focus.”

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