SOLUTION: Find the vertex, focus, directrix, and focal width of the parabola. x = 10y2 choices are below Vertex: (0, 0); Focus: one divided by forty comma zero ; Directrix: x = negative

Question 1135977: Find the vertex, focus, directrix, and focal width of the parabola.
x = 10y2
choices are below
Vertex: (0, 0); Focus: one divided by forty comma zero ; Directrix: x = negative one divided by forty ; Focal width: 0.1

Vertex: (0, 0); Focus: one divided by ten comma zero ; Directrix: x = negative one divided by ten ; Focal width: 0.1

Vertex: (0, 0); Focus: one divided by forty comma zero ; Directrix: x = one divided by forty ; Focal width: 40

Vertex: (0, 0); Focus: zero comma one divided by forty ; Directrix: y = negative one divided by forty ; Focal width: 40

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

is the standard equation for a right-left facing parabola with vertex at (, )
rewrite in the standard form :
.........both sides divide by

factor
....simplify

rewrite as

so, (, )= (, ),
parabola is symmetric around the x-axis and so the focus lies a distance from the center (, ) along the x-axis
(,)
(,)
(,)->focus
the distance between the focus and directrix is
parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance -p from the center left (,) x-coordinate

so, you have:
vertex at (, ),
focus at (,)
directrix is

you can use only this one of your choices as an answer
Vertex: (, );
Focus: (,);
Directrix: x = 1/40; -> this is incorrect, should be
Focal width:

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

For me, the most useful form of the equation of a parabola (that opens right or left) is

In this form...
(1) the vertex is (h,k);
(2) p is the (directed) distance from the vertex to the focus; which means -p is the directed distance from the vertex to the directrix; and
(3) 4p is the focal width (length of the latus rectum)

Written in that form, the equation in your example is

So...
(1) the vertex is (0,0);
(2) 4p=1/10 so p=1/40, so the focus is (1/40,0) and the directrix is x = -1/40; and
(3) the focal width is 4p = 1/10 = 0.1

The first answer choice is the correct one.
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