Question

Skylar is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by (y+5)^2=12(x+2), where x and y are measured in inches. What is the focus of the flashlight?

Answer 1

Answer: The focus of the flashlight= (1,-5)

Explanation:

Given: Skylar is designing a flashlight that uses a parabolic reflecting mirror and a light source.

The shape of the mirror can be modeled by

`(y+5)^2=12(x+2)`

We know that the standard form for the equation of parabola is
`(y-k)^2=4p(x-h)`, where focus = (h+p,k)

Rewrite the given equation in the standard form , we get

`(y-(-5))^2=4(3)(x-(-2))`

Therefore, focus of the flashlight=(-2+3,-5)=(1,-5)

Answer 2

From the equation of (y+5)^2=12(x+2), Focus is the distance(a) from the vertex(h,k).The equation is written in standard form, where 4a=12, solving for a
4a=12
a=3
The focus of the flashlight is found in 4th quadrant at the coordinates(1,-5).