Question

If a line passes through $(-3,0)$ and meet ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ at point $P$, then the reflected line passes through

• A. $(-3,0)$
• B. $(0,3)$
• C. $(3,0)$
• D. $(0,-5)$

Answer 1

The correct option is C $(3,0)$

Comparing given ellipse with standard ellipse

$a^2=25$ and $b^2=16$

So eccentricity, $e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}$

So coordinates of foci of the ellipse are $(\pm ae,0)=(\pm 3,0)$

Now using reflection property of ellipse, A ray passing through one focus

of an ellipse after reflection from ellipse it will pass through the another focus

Hence a line passing through $(-3,0)$ after reflection from the ellipse it will pass through $(3,0)$