Question

If a ray is incident on a parabolic mirror $y^2=4x$ along a line $y=6$ as shown, then what is the equation of the line along which the reflected ray travels?

• A. $9y=4x+18$
• B. $8y=6x–6$
• C. $3y=7x+13$
• D. $2x+3y=19$

Answer 1

The correct option is B $8y=6x–6$

In a concave mirror, When the incident is parallel to principal axis, then the reflected ray passes through the principal focus.

At the point of incidence, $y=6\Rightarrow x=9$

From the parabola equation $y^2=4ax$, focus is at $(1,0)$

So the reflected light must pass through $(1,0)$ and $(9,6)$

Therefore, from straight line equation, $(y-0)=\frac{6-0}{9-1}(x-1)$

we get, $8y=6x-6$

Hence, option $\left(b\right)$ is correct.