Find an equation for the parabola with vertex (6, 2) and focus (6, -1). A) x² - 12x + 12y + 12 = 0 B) x² - 12x - 12y + 12 = 0 C) y² - 12y - 12x + 12 = 0 D) y² + 12y + 12x + 12 = 0

Question

Quizplus · Accepted Answer

The vertex form of a parabola is $y = a(x-h)^2 + k$ for a parabola that opens up or down, and $x = a(y-k)^2 + h$ for a parabola that opens left or right, where $(h, k)$ is the vertex. Given the vertex (6, 2) and focus (6, -1), the parabola opens downward (since the focus is below the vertex), and its equation will be in the form of $y = a(x-h)^2 + k$. The distance between the vertex and the focus, which is 3 units, represents the value $|1/(4a)|$, indicating $a = -1/12$. Substituting $h = 6$, $k = 2$, and $a = -1/12$ into the vertex form gives the correct equation after rearranging and simplifying, which matches the form of choice A.

Find an Equation for the Parabola with Vertex (6, 2)