Question

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by (x-2)^2=10(y-3), where x and y are measured in inches. Where is the focus of the flashlight?

A. (–2, –0.5)
B. (2, –5.5)
C. (2, 5.5)
D. (5.5, 2)

Answer 1

We are given the parabolic equation
(x - 2)² = 10 (y - 3)
The general formula for the parabolic equation is
(x - h)² = 4a (y - k)
where a is the length of the focus
So,
4a = 10
a = 10/4
a = 2.5

The focus is 2.5

Answer 2

(2, 5.5)

Explanation:

The standard form of parabola is :

`(x - h)^2 = 4p (y - k)` ---1

where the focus is
`(h, k + p)`

Now we are Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source.The shape of the mirror can be modeled by:
`(x-2)^2=10(y-3)`

Now compare it with 1

`h = 2`

`k=3`

`4p=10`

`p=(10)/(4) =2.5`

Now Focus is
`(h, k + p)`

So, the focus of the flash light =
`(2,3+2.5)`

=
`(2,5.5)`

Hence the focus of the flashlight is (2, 5.5)