Point Satellite Single
parabola questions. please help!!?
1.) a satellite dish is shaped like a paraboloid. signals that strike the surface of the dish are reflected to a single point which corresponds to the focus of the parabola. this point is where the reciever should be located. suppose the dish is 10 feet across and 3 feet deep at its center, at what position should the reciever be placed?
2.) find all the values of b such that the parabola y=1/8×2 + bx+ 9/2 will have a diretrix having an equation of y=2.
3.) the locus of the midpoints of the segments joining the points of the parabola 4ay= x2 and the focus is also a parabola. find the vertex of the second parabola.
Taking the dish in std position The equation y^2 = 4ax is satisfied by (3, 5) so 25 = 12a this means a = 25/12.
So the gadget should be at 25/12 feet (what is this unit any way) from the center.
y=1/8×2 + bx+ 9/2 so 8y = x^2 +8bx +36,
8y = (x+4b)^2 +[36 - 16b^2]
This has point closet to x-axis if x = -4b. then
y = (36 – 16b^2)/8 which is 2
Hence 36 – 16b^2 = 16 etc. Now you can find b.
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