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# Algebra Examples

Step 1

Since the directrix is horizontal, use the equation of a parabola that opens left or right.

Step 2

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.

Step 2.2.1

Cancel the common factor of and .

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.

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

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

Subtract from .

Step 4

Substitute in the known values for the variables into the equation .

Step 5

Simplify.

Step 6