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1. Write an equation for an ellipse with foci (0, +4) and co-vertices (+ 2, 0).

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asked May 13, 2015 in PRECALCULUS by anonymous

1 Answer

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Step 1:

The foci of the ellipse is .

The co-vertices of the ellipse is .

Observe the foci.

x-coordinate are equal and lie on the y -axis, so the ellipse is vertical and center is at origin.

Ellipse equation :

The standard form of the vertical ellipse is image.

Where a is the length of the semi major axis, b is the length of the semi minor axis.

Here center of the ellipse is image.

Foci of the ellipse is image.

Vertices of the ellipse are image.

Co-vertices of the ellipse are image.

The distance between center and vertex is a.

The distance between center and focus is c.

The distance between center and co-vertex is b.

Condition is image.

Step 2:

The foci of the ellipse is .

The co-vertices of the ellipse is .

The distance between center and focus is image.

The distance between center and co-vertex is image.

Substitute image and image in image.

image

Therefore the vertices of the ellipse are image.

answered May 13, 2015 by joseph Apprentice

Contd...

Substitute image and image in the standard form of vertical ellipse.

image

Therefore the equation of the ellipse is image.

Solution :

The equation of the ellipse is image.

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