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JEE Main 20248 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
8 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2024 · 8 April · Evening Shift · Mathematics · Straight Lines

Let a ray of light passing through the point (3,10) reflects on the...

Let a ray of light passing through the point (3,10)(3,10) reflects on the line 2x+y=62 x+y=6 and the reflected ray passes through the point (7,2)(7,2). If the equation of the incident ray is ax+by+1=0a x+b y+1=0, then a2+b2+3aba^2+b^2+3 a b is equal to_________Let a ray of light passing through the point (3,10) reflects on the line 2 x+y=6 and the reflected ray passes through

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Step-by-step solution

Let a ray of light passing through the point (3,10) reflects on the line 2 x+y=6 and the reflected ray passes through
For B′x−72=y−21=−2(14+2−65)B^{\prime} \quad \frac{x-7}{2}=\frac{y-2}{1}=-2\left(\frac{14+2-6}{5}\right)x−72=y−21=−4x=−1y=−2B′(−1,−2)\begin{aligned} & \frac{x-7}{2}=\frac{y-2}{1}=-4 \\ & x=-1 \quad y=-2 \quad B^{\prime}(-1,-2)\end{aligned}incident ray $\mathrm{AB}^{\prime}\begin{aligned} & M_{\mathrm{AB}^{\prime}}=3 \\ & y+2=3(x+1) \\ & 3 x-y+1=0 \\ & a=3 b=-1 \\ & a^2+b^2+3 a b=9+1-9=1\end{aligned}$$$
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