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A ray of light along the line $\mathrm x=3$ is reflected at the ellipse $\mathrm {\frac{x^2}{25}+\frac{y^2}{16}=1.}$ The slope of the reflected ray is

Option: 1
$\frac{4}{15}$

Option: 2
$\frac{8}{15}$

Option: 3
$\frac{15}{8}$

Option: 4
$\frac{15}{4}$

Answers (1)

best_answer

The foci are $\mathrm {S_1(-3,0), S(3,0) }$ The line $\mathrm {x=3 }$ intersects the ellipse at
$\mathrm { \frac{y^2}{16}=1-\frac{9}{25}=\frac{16}{25}, y=\frac{16}{5} }$

The ray from $\mathrm { S(3,0) }$ to $\mathrm { P\left(3, \frac{16}{5}\right) }$ is reflected at $\mathrm { P }$ and passes through $\mathrm { S_1(-3,0)\\ }$

$\mathrm { \therefore \quad The \: \: slope \: \: of \: \: P S_1=\frac{16}{5} \times \frac{1}{(3+3)}=\frac{8}{15}. }$

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