a diagram of a paraboloid and a parabola

Okay, here's a problem involving conic sections:Problem:A satellite dish is shaped like a paraboloid, with a diameter of 10 meters and a depth of 2 meters. Where should the receiver be placed to receive the strongest signal?Solution:1. Understanding the Shape: A paraboloid is a three-dimensional shape formed by rotating a parabola around its axis of symmetry. The key property of a paraboloid is that all rays parallel to the axis of symmetry reflect to a single point, called the focus.2. Finding the Focus: We need to find the focus of this paraboloid. We can use the following formula for the distance from the vertex (the deepest point) to the focus of a parabola:• f = (1/4a)Where:• f is the distance from the vertex to the focus.• a is the coefficient of the squared term in the equation of the parabola.3. Finding 'a': Since the diameter is 10 meters, the radius is 5 meters. We know the depth is 2 meters. We can use this information to find the equation of the parabola. Assuming the vertex is at the origin (0