Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
-$$x ^ { 2 } = 40 y$$
A) focus: $( 0,10 )$
directrix: $y = - 10$
B) focus: $( 10,0 )$
directrix: $y = 10$
C) focus: $( 10,0 )$
directrix: $x = 10$
D) focus: $( 0 , - 10 )$
directrix: $\mathrm { x } = - 10$

Question

Quizplus · Accepted Answer

Since the parabola has its vertex at the origin and opens upward, we know that the focus will be located at (0, p) where p is the distance from the vertex to the focus. We can use the formula p = 1/(4a) where a is the coefficient of the squared term in the equation. In this case, a = 10, so p = 1/(4(10)) = 1/40. Therefore, the focus is at (0, 1/40).

To find the directrix, we know that it will be a horizontal line located a distance of p below the vertex (since the parabola opens upward). So the directrix is given by the equation y = -p = -1/40. Therefore, the correct choice is A.

Graph Parabolas with Vertices at the Origin Find the Focus x2=40yx ^ { 2 } = 40 yx2=40y

Graph Parabolas with Vertices at the Origin
Find the Focus $x ^ { 2 } = 40 y$