A satellite dish in the shape of a paraboloid opening upwards is 10 feet across, and 4 feet deep at its
vertex. How far is the receiver from the vertex, if it is placed at the focus? Round off your answer to the
nearest hundredths. Support your answer with a corresponding illustration.

The diagram above illustrates the satellite dish in the shape of an upward-opening paraboloid. The focus, where the receiver should be placed, is shown 1.56 feet above the vertex. 

If you have any further questions or need more details, feel free to ask.

Here are five related questions you might find interesting:
1. How would the position of the focus change if the dish were deeper?
2. What is the significance of the focus in the functionality of a satellite dish?
3. How would the parabola's equation change if the dish had a different width?
4. Can this method be used to design other parabolic reflectors, like for telescopes?
5. How does the shape of the paraboloid affect signal reception?

**Tip:** The focus of a parabola is crucial because it is the point where signals are concentrated after reflecting off the surface. In satellite dishes, this ensures optimal signal reception.

Learn how to calculate the distance from the vertex to the receiver in a parabolic satellite dish. Understand the geometry of parabolas and their application in satellite dish design. Suitable for high school students studying geometry and applications of parabolas.

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