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A light ray coming along the line $3 x + 4 y = 5$ gets reflected from the line $a x + b y = 1$ and goes along the line $5 x - 2 y = 10$ . Then,

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$a = \frac{64}{115}, b = \frac{112}{15}$

$a = \frac{14}{15}, b = \frac{- 8}{115}$

$a = \frac{64}{115}, b = \frac{- 8}{115}$

$a = \frac{64}{15}, b = \frac{14}{15}$

answer is C.

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Detailed Solution

$a x + b y = 1$ will be one of the bisectors of the given line. Equation of bisectors of the given lines are $\frac{3 x + 4 y - 5}{5} = \pm (\frac{5 x - 12 y - 10}{13})$

$\Rightarrow$ $64 x - 8 y = 115$ or $14 x + 112 y = 15$

$\Rightarrow$ $a = \frac{64}{115}, b - \frac{8}{115}$ or $a = \frac{14}{15}, b = \frac{12}{115}$

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