|
Question 1042105: a satellite dish has a shape called paraboloid where each cross section is a parabola since ratio signals (parallel to the x-axis will bounce off the surface of the dish to the focus the receiver should be placed at the focus.How far should the receiver be from the vertex if the dish is 12 ft across and 4.5 ft deep at the vertex?
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Same as #1041495;
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).
-
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.
|
|
|
| |
