SOLUTION: Sketch the following questions. Involving parabola.. A satellite dish has a shape called a paraboloid,where each cross-section is a parabola. Since radio signals (parallel

Question 1041495: Sketch the following questions. Involving parabola..
A satellite dish has a shape called a paraboloid,where each cross-section is a parabola. Since radio signals (parallel to the axis) will bounce off the surface of the dish to the focus, the receiver should be placed at the focus. How far should a receiver be from the vertex, if the dish is 12 ft. across 4.5 ft. deep at the vertex?
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Examine a cross section, having vertex imagined as a minimum if on a cartesian system. A point is ( 12/2, 4.5 ). TThe vertex at the origin. Recall, this is a parabola.

(1)
Change information into standard form equation for the parabola.

(2)
Find how far p, is the focus from the vertex, based on the typical model derived equation, ; this may require some care, but otherwise not too difficult.

--
Parabola with vertex as minimum, symmetry axis parallel to the y-axis, as standard form; vertex is (h,k).
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Using given focus and directrix to derive an equation for a parabola having symmetry axis parallel to the y-axis will be of a form , and the value p is how far the focus is from the vertex. Look at and study your lesson on this.
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