The ray is reflected so that the angle of incidence a between the incident ray and the tangent to the parabola at (a, b) is equal
to the angle of reflection between the reflected ray and the tangent (Snell's Law).
A. Using the pictures above as a guide, find an expression for the slope of the line supporting the
reflected ray as a function of a.
slope =
B. Find the slope-intercept equation of the line supporting the reflected ray.
C. Find the coordinates of the point F common to all the reflected rays (this is the property that
motivates parabolic antennas and reflectors). F is called the focus of the parabola.
D. Find the distance between (a, b) and F as a function of a. Simplify your answer.
Dp =
1
E. Let D be the line y = Find the distance between (a, b) and D as a function of a. The line
4
D is called the directrix of the parabola.
Dp