Question

A parabolic satellite television antenna has a diameter of 16 feet and is 1 foot deep. How far is the focus from the vertex

Answer 1

`P=16ft`

Explanation:

From the question we are told that:

Diameter
`d=16ft`

Depth
`dp=1ft`

Generally the equation for a Parabola is mathematically given by

`y=ax^2`

Since of the parabola has

Diameter
`d=16ft`

Depth
`dp=1ft`

Therefore it passes through

`x=(8,1)`

Therefore

`1=a(8)^2`

`a=(1)/(64)`

Since P(distance from focus to the vertex)

`a=(1)/(4p)`

Substituting

`(1)/(64)=(1)/(4p)`

`P=16ft`