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

Answer 1

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

Given parabola is, $(y-2{)}^2=4(x+1)$
Shifting origin $(-1,2)$ parabola is $Y^2=4X$, where $Y=y-2,X=x+1$
Thus focus of this parabola is $(X=1,Y=0)=(x+1=1,y-2=0)=(0,2)$
Fact: A ray after reflection from a parabolic mirror pass through it's focus.
Hence given line will pass through $(0,2)$