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?

F (2, 11/2)

Step-by-step explanation:

The expression:

(x-2) ² = 10 (y - 3)

can be rewritten in the vertex form as follows:

(x-2) ² = 10y - 30

(x-2) ² + 30 = 10y

1/10 (x-2) ² + 3 = y

General vertex form is:

y = a (x-h) ² + k

then, the vertex is locate at (h, k). In this case the vertes is (2, 3), and a = 1/10

The focus of a parabola is located ar F (h, k+p), where p = 1 / (4a). Replacing into these equations:

p = 1 / (4*1/10) = 5/2

F (2, 3+5/2) = F (2, 11/2)