A ray emerging from the point (5, 0) is incident on the hyperbola `9x^2-16 y^2=144`
at the point `P`
with abscissa 8. Find the equation of the reflected ray after the first
reflection if point `P`
lies in the first quadrant.
Text Solution
Verified by Experts
Given hyperbola is `(x^(2))/(16)-(y^(2))/(9)=1" (1)"` Here, a = 4 and b = 3. So, foci and `(pmsqrt(a^(2)+b^(2)),0)-=(pm5,0).` Incident ray through `F_(1)(5, 0)` strikes the ellipse at point `P(8, 3sqrt3)`. Therefore, reflected ray will go through another focus `F_(2)(-5,0).` So, reflected ray is line through points `F_(2) and P`, which is `3sqrt3x-13y+15sqrt3=0.`
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