Question

A ray of light travels along a line $y=4$ and strikes the surface of a curves $y^2=4(x+y)$, then equation of the line along which reflected ray travels is

• A. $x=0$
• B. $x=2$
• C. $x+y=4$
• D. $2x+y=4$

Answer 1

Answer: (A)

$x=0$

Given equation of parabola is
$y^2-4y=4x$
$(y-2{)}^2=4(x+1)$
Vertex is at $(-1,2)$
Focus is at $(0,2)$
Point of intersection of the curve and $y=4$ is $(0,4).$
From the reflection property of parabola, reflected ray passes through the focus.
$\Rightarrow x=0$ is required line.