Algebra Examples

Find the Parabola with Focus (0,0) and Directrix y=-6 (0,0) y=-6
Step 1
Since the directrix is vertical, use the equation of a parabola that opens up or down.
Step 2
Find the vertex.
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Step 2.1
The vertex is halfway between the directrix and focus. Find the coordinate of the vertex using the formula . The coordinate will be the same as the coordinate of the focus.
Step 2.2
Simplify the vertex.
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Step 2.2.1
Cancel the common factor of and .
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Step 2.2.1.1
Factor out of .
Step 2.2.1.2
Factor out of .
Step 2.2.1.3
Factor out of .
Step 2.2.1.4
Cancel the common factors.
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Step 2.2.1.4.1
Factor out of .
Step 2.2.1.4.2
Cancel the common factor.
Step 2.2.1.4.3
Rewrite the expression.
Step 2.2.1.4.4
Divide by .
Step 2.2.2
Subtract from .
Step 3
Find the distance from the focus to the vertex.
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Step 3.1
The distance from the focus to the vertex and from the vertex to the directrix is . Subtract the coordinate of the vertex from the coordinate of the focus to find .
Step 3.2
Add and .
Step 4
Substitute in the known values for the variables into the equation .
Step 5
Simplify.
Step 6