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JEE Main 20139 AprilOnline
Exam
JEE Main
Year
2013
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2013 · 9 April · Online · Mathematics · Straight Lines

A light ray emerging from the point source placed at P(1,3) is...

A light ray emerging from the point source placed at P(1,3)\mathrm{P}(1,3) is reflected at a point Q\mathrm{Q} in the axis of xx. If the reflected ray passes through the point RR (6,7)(6,7), then the abscissa of QQ is:A light ray emerging from the point source placed at P(1,3) is reflected at a point Q in the axis of x . If theA light ray emerging from the point source placed at P(1,3) is reflected at a point Q in the axis of x . If the

Options

  1. A1
  2. B3
  3. C72\frac{7}{2}
  4. D52\frac{5}{2}

Correct answer

D. 52\frac{5}{2}

Step-by-step solution

Let abcissa of Q=x\mathrm{Q}=x A light ray emerging from the point source placed at P(1,3) is reflected at a point Q in the axis of x . If the
∴Q=(x,0)tan⁡θ=0−7x−6,tan⁡(180∘−θ)=0−3x−1\begin{aligned} \therefore \quad & Q=(x, 0) \\ & \tan \theta=\frac{0-7}{x-6}, \tan \left(180^{{}^{\circ}}-\theta\right)=\frac{0-3}{x-1}\end{aligned} Now, tan⁡(180∘−θ)=−tan⁡θ\tan \left(180^{{}^{\circ}}-\theta\right)=-\tan \theta \therefore \quad −3x−1=−7x−6⇒\frac{-3}{x-1}=\frac{-7}{x-6} \Rightarrowx=52\frac{5}{2}
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