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Q.
A light ray coming along the line $3x + 4y = 5$ gets reflected from the line $a x + b y = 1$ and goes along the line $5x- 12 y = 10$. Then,
Straight Lines
Solution:
$ax + by = 1 $ will be one of the bisectors of the given line. Equations of bisectors of the given lines are
$\frac{3x+4y-5}{5} = \pm\left(\frac{5x-12y-10}{13}\right)$
or $64 x - 8y = 115$
or $14 x + 112 y = 15$
or $a = \frac{64}{115}, b = -\frac{8}{115}$
or $a = \frac{14}{15}, b = \frac{12}{115}$