Answer to Question #184228 in Analytic Geometry for Sherine Horo

Question

find the shape of a c curved mirror such that lightfrom the source at the origin will be reflected in a beam of rays parallel to x-axis.

Answer 1

The mirror of course would be a spherical section. Further, since convex mirror converges a beam of rays to a point, and a conscave mirror diverges, the mirror will be a concave one.

But how to obtain the shape of the mirror in terms of focus (a,0), say, of a parabola?

The spherical mirror is only approximately the correct answer. The property you want is only given by a parabolic mirror.

From the Wikipedia page I can quote that the relation is 4fy=x^2

4fy=x^2 where f

f is the distance of the focus to the origin of the parabola.

Your focus is at (a,0)

(a,0), so the equation would be 4ax=y^2

4ax=y^2. You can solve that equation for y

y and have a function y=f(x)= √(4ax)