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?

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

Step-by-step 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

We know that the standard form for the equation of parabola is , where focus = (h+p,k)

Rewrite the given equation in the standard form , we get

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

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: