Question
An engineer designs a satellite dish with a parabolic cross section. The dish is 14 ft wide at the opening, and the focus is placed 4 ft from the vertex.
a) Position a coordinate system with the origin
at the vertex and the x-axis on the parabola's
axis of symmetry and find an equation of the
parabola.
b) Find the depth of the satellite dish at the vertex.
a) Position a coordinate system with the origin
at the vertex and the x-axis on the parabola's
axis of symmetry and find an equation of the
parabola.
b) Find the depth of the satellite dish at the vertex.
Answers
Scott
the general equation is
... x = a(y - k)^2 + h
the vertex is at the origin, so h and k are both zero
a = 1 / 4p
... where p is the distance from the vertex to the focus
b) the center depth is the value of x at the edges of the dish (where y equals ±7)
... x = a(y - k)^2 + h
the vertex is at the origin, so h and k are both zero
a = 1 / 4p
... where p is the distance from the vertex to the focus
b) the center depth is the value of x at the edges of the dish (where y equals ±7)