Question

ABC is a parabolic mirror, and PQ is a ray of light traveling parallel to the X axis, which is also the axis of the parabolalight takes the path that is the shortest.if thats the case, prove that the light gets reflected off and passes through the focus of the parabola.the vertical line is the directrix of the parabola.write the proof?​

Answer 1

Example:

Given parabola is (y−2)

2

=4(x+1)

⇒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)

⇒(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.