Question

A ray emanating from the point $( - 3,0)$ is incident on the ellipse $16x^{2} + 25y^{2} = 400$ at the point P with ordinate 4. Then the equation of the reflected ray after first reflection is

• A. $4x + 3y = 12$
• B. $3x + 4y = 12$
• C. $4x - 3y = 12$
• D. $3x - 4y = 12$

Answer 1

Answer: (A)

$4x + 3y = 12$

Answer 2

For point P y-coordinate =4

Given ellipse is $16x^{2} + 25y^{2} = 400$

$16x^{2} + 25(4)^{2} = 400$, ∴ $x = 0$

∴ co-ordinate of P is (0, 4)

$e^{2} = 1 - \frac{16}{25} = \frac{9}{25}$

∴ $e = \frac{3}{5}$

∴ Foci $( \pm ae,0)$ , i.e. $( \pm 3,0)$

∴ Equation of reflected ray $(i.e.PS)$ is $\frac{x}{3} + \frac{y}{4} = 1$or

$4x + 3y = 12$