Question

A ray of light coming from the point $P\equiv (2,3)$ is reflected at a point $Q$ on the $x$- axis and then passes through the point $R\equiv (4,5)$. The equation of $PQ$ is

• A. $x+y=5$
  
• B. $3x-y=3$
• C. $4x+y=11$
• D. $2x+y=7$

Answer 1

The correct option is C $4x+y=11$

Let $Q$ be the point of intersection of incident ray and $x-$axis, image of $R$ w.r.t $x-$ axis , $R^{\prime }\equiv (4,-5)$


$\because P,Q,R^{\prime }$ are collinear
So,equation of $P{R}^{\prime }$ or$PQ$ by Point-slope form is $y-3=-4(x-2)$
$\Rightarrow 4x+y=11$