IXL - Convert equations of conic sections from general to standard form (Precalculus practice)

The equation of a parabola is

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Write the equation in vertex form.

Write any numbers as integers or simplified proper or improper fractions.

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question

Write the equation in standard form for the hyperbola

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100

key idea

The equation of a hyperbola that has a vertical orientation in standard form is:

(

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)

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(

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)

The center is

(

)

the vertices are

(

)

and the co-vertices are

(

)

Note that the vertices are on the hyperbola, but the co-vertices are not.

The transverse axis is the line segment with endpoints at the vertices and has length

The conjugate axis is the line segment with endpoints at the co-vertices and has length

(

)

(

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)

(

)

(

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)

(

)

solution

To write the equation in standard form, make sure the terms with

and

are on the left side of the equation and the constant is on the right. Then, divide by the constant.

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100

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100

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100

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Teacher tools

Work it out

Not feeling ready yet? These can help:

DD.7Convert equations of parabolas from general to vertex form

EE.5Convert equations of circles from general to standard form

FF.6Convert equations of ellipses from general to standard form

GG.8Convert equations of hyperbolas from general to standard form

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