Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0), focus (0, - $4$ )
A) $x ^ { 2 } = 4 y$
B) $y ^ { 2 } = - 17 x$
C) $x ^ { 2 } + y ^ { 2 } = 16 y$
D) $x ^ { 2 } = - 16 y$
E) $x ^ { 2 } = - y$

Question

Quizplus · Accepted Answer

A parabola with vertex at the origin that opens downwards has an equation of the form $x^2=-4py$, where $p$ is the distance between the vertex and the focus. In this case, $p=4$ since the focus is located at $(0,-4)$. Thus, the equation of the parabola is $x^2=-16y$, which matches choice D.

Find an Equation for the Conic That Satisfies the Given 444

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