IXL - Write equations of hyperbolas in standard form using properties (Algebra 2 practice)

Write the equation in standard form for the hyperbola with vertices

(

–

)

and

(

)

and a conjugate axis of length 8.

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question

Write the equation in standard form for the hyperbola with vertices

(

–

)

and

(

)

and a conjugate axis of length 6.

key idea

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

(

–

)

–

(

–

)

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

(

)

(

–

)

(

)

(

–

)

(

)

solution

To write the equation in standard form, find the center. Then, use the vertices to find the value of

and determine if the hyperbola has a horizontal or vertical orientation. Finally, use the length of the conjugate axis to find the value of

Find the center.

The vertices are the endpoints of the transverse axis and the center is the midpoint of the transverse axis. Since one vertex is 9 units left of the origin and the other is 9 units right, their midpoint is the origin. So, the center is

(

)

Find

and determine the orientation.

The distance from the center to each vertex is

So,

Also, since the vertices are on the line

the transverse axis is horizontal and the hyperbola has a horizontal orientation.

Find

The length of the conjugate axis is 6. Since

is half this length,

Write the equation in standard form.

The equation of the hyperbola in standard form is:

(

–

)

–

(

–

)

Hyperbola with a horizontal orientation

(

–

)

–

(

–

)

Plug in

and

Plug in

and

–

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Teacher tools

Work it out

Not feeling ready yet? These can help:

GG.6Write equations of hyperbolas in standard form from graphs

M.4Distance between two points

B.10Midpoint formula: find the midpoint

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