Section 4.2 states that if a source of electromagnetic energy is placed at the focus of the paraboloid, and if the paraboloid is a reflecting surface, then the wave will bounce back in lines parallel to the axis of the paraboloid. To demonstrate this, consider the parabola y² =2px shown in Figure 4.12. Let  P(x₁,y₁) be a point on the parabola, and PF be the line from P to the focus. Construct the line L through P parallel to the_  x-axis and the line M tangent to the parabola at P. The angle between L and M is β and the angle between PF and M is The angle is the angle at which a ray from F strikes the parabola at P. Because the angle of incidence equals the angle of reflection, the ray reflected from P must be at an angle to M. Thus, if we can show that α =β we have demonstrated that rays reflected from the parabola starting at F will be parallel to the x-axis

a. First show that tan β =(p/y₁).

b. Now show that tan α = (p/y₁). which demonstrates that

Figure 4.12