Question

A ray of light moving parallel to the $x$-axis gets reflected from a parabolic mirror whose equation is ${(y-2)}^2=4(x+1)$. After reflection, the ray must pass through the point

• A. $(0,2)$
• B. $(2,0)$
• C. $(0,-2)$
• D. $(-1,2)$

Answer 1

The correct option is A $(0,2)$

Given parabola is ${(y-2)}^2=4(x+1)$
$\Rightarrow Y^2=4aX$ where $X=x+1,Y=Y-2,a=1$
We know focus of parabola $Y^2=4aX$ is $(X=-a,Y=0)$
$\Rightarrow (x+1=1,y-2=0)=(0,2)$
Thus focus of the given parabola is $(0,2)$

We know every reflected ray from parabolic mirror passes through its focus. Hence option 'A' is correct choice.