If the disk is 3 meters in diameter, what is the depth of the disk ?
A satellite dish has its receiver at the focus of a parabolic disk. The focus is 50 cm from the vertex of the disk.
Imagine the satellite dish is a parabola with its vertex at the origin facing up.
You should remember the standard equation of parabola such that:
`(y-k)^2 = 4p(x - h)`
Since the satellite dish is a parabola whose vertex is at origin and it is facing up, hence, you may adapt the equation of parabola to these conditions such that:
`(x - h)^2 = 4p(y - k)`
Since (h,k) represent the vertex of parabola and since the problem provides the information about the location of vertex of parabola, you may substitute 0, 0 for h and k such that:
`x^2 = 4py`
Notice that p represents the distance between the vertex and focus, hence, you may substitute 50 for p such that:
`x^2 = 4*50*y => x^2 = 200y`
Since the problem provides the diameter of the dish, hence, you may consider `x = +-d/2` .
Notice that the units of measure of diameter and the units of measure of distance p are different , hence, you should convert the meters in centimeters such that:
`d = 3 m => d = 300 cm => x = +-300/2 cm = +-150 cm`
Substituting 150 for x in equation of parabola yields:
`150^2 = 200 y => 225*100 = 200 y => 225 = 2y => y = 225/2`
`y = 112.5 cm`
Hence, evaluating the depth of the disk under the given conditions yields `y = 112.5 cm` .