Question

A ray of light passes through A(1,2) gets reflected-at point B on x axis and num passes through (5 , 3) find equation of AB.

Answer 1

As angle of incidence$=$angle of reflection

$\Rightarrow \tan \theta =\tan \theta$

$\Rightarrow \frac{(\alpha -1)}{2}=\frac{5-\alpha }{3}$

$\Rightarrow 3\alpha -3=10=2\alpha$

$\Rightarrow 5\alpha =13$

$\Rightarrow \alpha =\frac{13}{5}$

Equation of AB: $y-0=\frac{0-2}{\frac{13}{5}-1}(x-\frac{13}{5})$

$\Rightarrow y=\frac{-2\times 5}{8}\left(\frac{5x-13}{5}\right)$

$\Rightarrow 4y=-10x+26$

$\Rightarrow 2y=-5x+13$.