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

Answer:

(2, 5.5)

Step-by-step 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

$h = 2$

$k=3$

$4p=10$

$p=\frac{10}{4} =2.5$

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)