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Find the Center,foci,vertices, and eccentricity of the ellipse, and sketch its graph.

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Find the <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Center,foci,vertices, and eccentricity of the ellipse, and sketch its graph.

asked Feb 17, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The ellipse equation is image.

Convert the equation into standard form of ellipse by using completing square method.

image

image

image

To change the expressions image and image into a perfect square trinomial, add (half the x coefficient)² and add (half the y coefficient)² to each side of the equation

image

image

image

image

image

Compare with standard form of vertical ellipse is .

Where image

image  is length of semi major axis and image is length of semi minor axis.

Center is , vertices

Foci and image.

Where .

image

In this case image.

Center image

Vertices image

Co-vertices image

image

Focus image

image

Eccentricity image.

Graph:

Draw the coodinate plane.

Plot the center, vertices, co-vertices and foci of the ellipse.

Then sketch the ellipse by using the semi major axis length is 3 units and semi minor axis length is 2 units.

Solution:

Center image

Vertices image

Focus image

Eccentricity image.

Graph of ellipse:

.

answered Feb 23, 2015 by david Expert

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