question_answer

A ray of light is incident along a line which meets another line, \[7x-y+1=0\], at the point (0, 1). The ray is then reflected from this point along the line, \[y+2x=1\]. Then the equation of the line of incidence of the ray of light is   JEE Main Online Paper (Held On 10 April 2016)

A) \[41x+38y-38=0\]               

B) \[41x-38y+38=0\]

C) \[41x+25y-25=0\]0             

D) \[41x-25y+25=0\]

Correct Answer: B

Solution :

             In cidene lines \[{{L}_{1}}+\lambda {{L}_{2}}=0\] \[(7x-y+1)+\lambda (y+2x-1)=0\] Let a point (1, - 1) on \[y+2x=1\] And image of (1, .1) lie on incidence line in\[7x-y-+1=0\] \[\frac{x-1}{1}=\frac{y+1}{-1}=\frac{-2(7+1+1)}{50}=x=\frac{-38}{25},\,\,\,\,y=\frac{-16}{25}\] \[\left( 7\left( \frac{-38}{25} \right)+\frac{16}{25}+1 \right)+\lambda \left( \frac{-16}{25}-\frac{76}{25}-1 \right)\] \[\lambda =\frac{-225}{117}\] \[(7x-y+1)\frac{-225}{117}(y+2x-1)=0\]              \[369x-342y+342=0\]              \[41x-38y+38=0\]