AnswersPrecalculusModeling with Conic Sections and Polar Equations — TestQuestion 11
11
QuizMultiple Choice

Modeling with Conic Sections and Polar Equations — Test

Question 11 • Precalculus

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by open paren x minus 2 close paren squared is equal to 10 times open paren y minus 3 close paren , where x and y are measured in inches. Where is the focus of the flashlight?

Answer
A
open paren 2 comma negative 5 point 5 close paren
B
open paren 5 point 5 comma 2 close paren
C
open paren 2 comma 5 point 5 close paren
D
open paren negative 2 comma negative 0 point 5 close paren

Explanation

Compare the equation (x − 2)² = 10(y − 3) with the standard parabola form (x − h)² = 4p(y − k). The vertex is (2, 3), and 4p = 10, so p = 2.5. Since the parabola opens upward, its focus is p units above the vertex: (2, 3 + 2.5) = (2, 5.5), choice C.

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