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,

Options

A. `a=(14)/(15), b=(112)/(15)`
B. `a=(14)/(15), b=-(18)/(115)`
C. `a=(64)/(115), b=-(8)/(115)`
D. `a=(64)/(15), b=(14)/(15)`

Answer

C

Explanation

ax+by=1 will be one of the bisectors of the given line.
Bisectors of the given lines are
`(3x+4y-5)/(5)=+-((5x-12y-10)/(13))`
`rArr 64x-8y=115 " or " 14x+112y=15`
`therefore a=(64)/(115),b=-(8)/(115) "or a =(14)/(15), b =(112)/(15)`