IXL - Find properties of ellipses (Precalculus practice)

The graph shows an ellipse. What are its vertices?

and

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Learn with an example

question

The graph shows an ellipse. What are its vertices?

and

key idea

An ellipse is the set of points in a plane such that the sum of the distances from two fixed points, called the

foci,

is constant. Each of the foci is called a

focus.

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.

The equation of an ellipse that has a horizontal orientation in standard form is

(

–

)

(

–

)

where

The center is

(

)

the vertices are

(

)

and the co-vertices are

(

)

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

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

solution

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. Since the center is

(

)

the major axis is on the horizontal line

Locate the vertices.

The vertices are

(

–

)

and

(

)

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Teacher tools

Work it out

Not feeling ready yet? These can help:

FF.2Find the length of the major or minor axis of an ellipse

FF.1Find the center, vertices, or co-vertices of an ellipse

FF.3Find the foci of an ellipse

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