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)

14

step-by-step explanation:

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