IXL - Write equations of ellipses in standard form (Precalculus practice)

The graph shows an ellipse. Write its equation in standard form.

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question

The graph shows an ellipse. Write its equation in standard form.

key idea

An ellipse that has a horizontal orientation is wider than it is tall. An ellipse that has a vertical orientation is taller than it is wide.

solution

Locate the center.

The center is

(

–

)

The ellipse is wider than it is tall, so it has a horizontal orientation. This means the major axis is horizontal and the minor axis is vertical. To find

count the units from the center to the ellipse along the major axis. To find

count the units from the center to the ellipse along the minor axis.

So,

and

The equation of the ellipse in standard form is:

(

–

)

(

–

)

Ellipse with a horizontal orientation

(

–

)

(

–

)

Plug in

–

and

Plug in

–

and

(

)

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Not feeling ready yet? These can help:

U.7Find properties of ellipses

FF.4Write equations of ellipses in standard form from graphs

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