Choose the one alternative that best completes the statement or answers the question.
A model of the form $x ^ { 2 } = 4 p y$ is given. Identify the focus, and write an equation for the directrix.
-$$x ^ { 2 } = 32 y$$
A) focus: $( 0,8 )$; directrix: $y = - 8$
B) focus: $( 8,0 )$; directrix: $y = - 8$
C) focus: $( - 8,0 )$; directrix: $y = 8$
D) focus: $( 0 , - 8 )$; directrix: $y = 8$

Question

Quizplus · Accepted Answer

The given equation $x^2 = 32y$ is in the form $x^2 = 4py$, where $4p = 32$, so $p = 8$. The focus of a parabola in this form is $(0, p)$, which is $(0, 8)$, and the directrix is $y = -p$, which is $y = -8$.

Choose the One Alternative That Best Completes the Statement or Answers