Question

Identify the directrix, focus, and vertex of the parabola in the figure.

(Image Attached Below in Pic 1)

Directrix
^(0,4), (-3, 2), (-3, 3), y = 4, (1,-1), x = 4

Focus
^(0,4), (-3, 2), (-3, 3), y = 4, (1,-1), x = 4

Vertex
^(0,4), (-3, 2), (-3, 3), y = 4, (1,-1), x = 4
__________________________________________

2) Identify the directrix, focus, and vertex of the parabola in the figure.

(Image Attached Below in Pic 2)

Match the correct coordinates or equation with the correct part of the parabola.

Directrix
^(2, -4), y = -6, x = -6, (6, -1), (2, -5), (0, -6)

Focus
^(2, -4), y = -6, x = -6, (6, -1), (2, -5), (0, -6)

Vertex
^(2, -4), y = -6, x = -6, (6, -1), (2, -5), (0, -6)

Answer 1

1) Directrix is y=4, focus is (-3,2), and vertex is (-3,3).

• Focus and vertex are given to you
• The vertex is equidistant from the focus and the directrix. Since the distance from the vertex to the focus is 1, the distance from the vertex to the directrix must also be 1, giving its equation to be y=4.

2) Directrix y=-6, focus (2,-4), vertex (2,-5)

• Focus and vertex are given to you
• The vertex is equidistant from the focus and the directrix. Since the distance from the vertex to the focus is 1, the distance from the vertex to the directrix must also be 1, giving its equation to be y=-6.