9-28 Graphing Ellipse An equation of an ellipse is given. (a) Find the vertices, foci and eccentricity of the ellipse. (b) Determine the lengths of the major and minor axes. (c) Sketch a grapg of the ellipse.
The vertices, foci and eccentricity of the given equation of ellipse.
The given equation of an ellipse is,
The basic equation for an ellipse with a horizontal major axis which is used is as follows,
Here, and are constant values.
Expression to find vertices is,
Expression to find Foci is,
Expression to find Eccentricity ,
Consider the given equation of the ellipse,
To express the above equation as the basic equation of ellipse, divide by on both side,
Compare the above equation with the basic equation for an ellipse and find the vertices as follows,
Find the vertices,
The lengths of the major and minor axes.
A graph of the given equation of the ellipse.
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