Straight Lines
Reflection of Ray — Incident Ray Equation
nta_pyq_2024_apr
Grade 11
Question:
Let a ray of light passing through the point $(3,10)$ reflects on the line $2x+y=6$ and the reflected ray passes through the point $(7,2)$. If the equation of the incident ray is $ax+by+1=0$, then $a^2+b^2+3ab$ is equal to _____
Step-by-Step Solution
Key Concept: Find the image $B'$ of $B(7,2)$ in the line $2x+y-6=0$: $\frac{x-7}{2}=\frac{y-2}{1}=-2\cdot\frac{14+2-6}{5}=-4$. So $B'=(-1,-2)$.
Image of $(7,2)$ is $(-1,-2)$. Incident ray: $3x-y+1=0$. $a^2+b^2+3ab=1$.
Correct Answer: 1