Question

a satellite dish is shaped like a paraboloid of revolution. this means that it can be formed by rotating a parabola around its axis of symmetry. the receiver is to be located at the focus. if the dish is 56 feet across at its opening and 7 feet deep at its center, where should the receiver be placed? find the equation of the parabola. how far above the vertex should the receiver be placed?

Explanation:

Step1: Set up parabola equation

Let vertex be at (0,0), parabola opens up: $x^2 = 4py$.

Step2: Find point on parabola

Dish is 56ft across (radius 28ft) and 7ft deep: (28,7) is on parabola.

Step3: Solve for p

Substitute (28,7) into equation: $28^2 = 4p(7)$
$784 = 28p$
$p = \frac{784}{28} = 28$

Answer:

The receiver should be placed 28 feet above the vertex.