Find focus, directrix and

For the parabola x = (-1/8)y^2, find the focus, directrix, and axis of symmetry.

Frist rewrite equation in standard form:

-8x = y^2

Equation is now in the form y^2 = 4px

Where p=-2, focus is (p, 0) and directrix is x=-p.

So the foucs is (-2, 0)
The directrix is x=2
And because y is squared the axis of symmetry is the x-axis

Hope that helps!

x = - 1/8 y²

The equation is in the vertex form, x = a(y - k)² + h, where (h, k) is the vertex, or

x = - 1/8(y - 0)² + 0

Vertex (0, 0)
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Since the equation is x as a function of y, the parabola will be horizontally oriented and, since 'a' is negative, it will open to the left.

a = - 1/8

p = 1 / 4a
p = 1 / 4(- 1/8)
p = 1 / (- 4/8)
p = 1 / (- 1/2)
p = - 2

Since the parabola opens to the left, the focus will be to the left of the vertex and, since p is a distance...not a value, its sign is inconsequential.

Focus (Fx, Fy):

Fx = h - | p |
Fx = 0 - 2
Fx = - 2

Fy = k
Fy = 0

Focus (- 2, 0)
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Since the parabola opens to the left, the directrix will be to the right of the vertex.

Directrix:

x = h + | p |
x = 0 + 2
x = 2

Directrix: x = 2
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Axis of Symmetry:

x = h
x = 0
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