SOLUTION: Find the vertex, focus, directrix, and focal width of the parabola. choices below (5 points) negative 1 divided by 16 times x squared = y Vertex: (0, 0); Focus: (0, -4); Directr

Algebra ->  Trigonometry-basics -> SOLUTION: Find the vertex, focus, directrix, and focal width of the parabola. choices below (5 points) negative 1 divided by 16 times x squared = y Vertex: (0, 0); Focus: (0, -4); Directr      Log On


   

Question 1138077: Find the vertex, focus, directrix, and focal width of the parabola. choices below (5 points)
negative 1 divided by 16 times x squared = y
Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16

Vertex: (0, 0); Focus: (-8, 0); Directrix: x = 4; Focal width: 64

Vertex: (0, 0); Focus: (0, 4); Directrix: y = -4; Focal width: 4

Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 64
Answer by MathLover1(20850) About Me  (Show Source):
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Find the vertex, focus, directrix, and focal width of the parabola. choices below
-%281%2F+16%29x%5E2+=+y
The standard form is %28x+-+h%29%5E2+=+4p+%28y+-+k%29, where the focus is (h,+k+%2B+p) and the directrix is y+=+k+-+p.
given:
-%281%2F+16%29x%5E2+=+y
x%5E2+=+%281%2F%281%2F-16%29%29y
x%5E2+=+-16y
=>h=0,k=0=>the vertex at:(0, 0)
+4p=-16=>p=-4
a focus at (h, k+%2B+p)=(0, -4)
a directrix at y+=+k-p=>y=0+-+%28-4%29=4

The focal width of a parabola is the length of a segment that is parallel to the directrix and passing through the focus of a parabola. The length of this segment is 4p units, or four time the length from the focus to the vertex.
focal width:16

answer:Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16