Question 1198216
**1. Find the Equation of the Parabola**

* **Vertex:** (0, -6) 
* **Point on the Parabola:** (36, 0) (Since the dish is 72 feet across, the point on the parabola is half of that, or 36 feet, from the vertex)

* **Standard Form of a Parabola:** 
   (x - h)² = 4p(y - k) 
   where (h, k) is the vertex

* **Substitute values:** 
   (x - 0)² = 4p(y - (-6)) 
   x² = 4p(y + 6)

* **Find the value of 'p':**
   Substitute the point (36, 0) into the equation:
   36² = 4p(0 + 6)
   1296 = 24p
   p = 1296 / 24
   p = 54

* **Equation of the Parabola:** 
   x² = 4 * 54 * (y + 6)
   x² = 216(y + 6)

**2. Find the Distance of the Receiver from the Vertex**

* The receiver should be placed at the focus of the parabola.
* The distance from the vertex to the focus is 'p'.

* **Receiver Distance:** 54 feet

**Therefore:**

* The equation of the parabola is: x² = 216(y + 6)
* The receiver should be placed 54 feet above the vertex of the dish.