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Math word problem Help?
A satellite is shaped like a paraboloid of revolution. the Signals that emanate from the satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. if the dish is 14 feet across the opening and 4 feet deep at its center, at what position should the receiver be placed?
1 Answer
- ?Lv 78 years ago
parabola vertex form
y= a(x-h)^2 + k => symmetry: x = h
or x = a(y-k)^2 + h => symmetry: y = k
(h,k) => vertex
a = 1/4c
c : distance between vertex and focus or directrix.
..................................................................................................................
let the vertex of the satellite be (0,0), the edge of satellite will be at (7,4)
y = a(x-0)^2 + 0
4 = a*7^2
a = 4/49 = 1/4c
c = 49/16
then
the focus will be at (0, 49/16)