IXL - Find the foci of an ellipse (Algebra 2 practice)

What are the foci of the ellipse

Write your answer in simplified, rationalized form.

and

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Learn with an example

question

What are the foci of the ellipse

Write your answer in simplified, rationalized form.

and

key idea

The equation of an ellipse that has a vertical 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

The distance from the center to each focus is

where

–

The foci lie on the major axis. If the ellipse has a vertical orientation, the coordinates of the foci are

(

)

solution

To find the foci, first find the center

(

)

Then, calculate the distance from the center to the foci, which is

Find the center.

Use the equation in standard form to identify the center.

(

–

)

(

–

)

The center is

(

)

which is the origin.

Calculate

Start by identifying

and

Since

must be 75 and

must be 39. Calculate

then take the square root.

–

Since

is a distance, it is positive. So

Write the foci.

Since the ellipse has the form

(

–

)

(

–

)

where

it has a vertical orientation. This means you should add and subtract

from the

-coordinate

of the center to find the foci. So, the foci are

(

)

(

)

and

(

–

)

(

–

)

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

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