Question

From the focus of the parabola y²=12x, a ray of light is directed in a direction making an angle \(tan^{-1}\frac{3}{4}\)  with the x-axis. Then the equation of the line along which the reflected ray leaves the parabola is

• A. y=2
• B. y=18
• C. y=9
• D. y=36

Answer 1

The Correct Option is B

The correct answer is option (B): y=18

Answer 2

Here, \(a = 3\)
So, the coordinates of the focus are (3, 0).
Let \(A\) be the focus of the parabola and \(AB\) be the incident ray and \(BC\) be the reflected ray.
Slope of \(AB = \tan\theta = \frac{3}{4}\)
Equation of \(AB\) is:
\(y - 0 = \frac{3}{4}(x - 3)\)
\(4y = 3x - 9\)
Let the coordinates of \(B\) be \(\left(\frac{a^2}{12}, a\right)\).
Now,
\(4\alpha = \frac{3\alpha^2}{12} - 9\)
\(16\alpha = \alpha^2 - 36\)
\(\alpha^2 - 16\alpha - 36 = 0\)
\(\alpha = 18\) [Neglecting \(\alpha = -2\)]
The reflected ray leaves the parabola at \(y = 18\).