Question

A ray passing through $(\sqrt{\frac{5}{6}},0)$ strikes the surface of the curve $2x^2+3y^2=5$ and gets reflected then reflected ray will pass through

• A. $(-\sqrt{\frac{5}{6}},0)$
• B. $(0,\sqrt{\frac{5}{6}})$
• C. $(5,6)$
• D. None of these

Answer 1

Answer: (A)

$(-\sqrt{\frac{5}{6}},0)$

Given equation is $2x^2+3y^2=5$

$\Rightarrow \frac{2x^2}{5}+\frac{3y^2}{5}=1$

So, compairing with the general equation,

$a^2=\frac{5}{2}$ and $b^2=\frac{5}{3}$

ie, The coordinates of the focii are $(\pm \sqrt{a^2-b^2},0)$

$\Rightarrow (\pm \sqrt{\frac{5}{2}-\frac{5}{3}},0)\Rightarrow (\pm \sqrt{\frac{5}{6}},0)$

So, the rays are coming from one of the focii of the ellipse.

Then according to the reflection property of the ellipse,

The reflected rays go through the other focii.

ie, $(-\sqrt{\frac{5}{6}},0)$

Thus option A is correct.