55–64 ■ Finding the Equation of a Conic Find an equation for the conic section with the given properties.
The ellipse with vertices and and passing through the point .
The equation for the ellipse with vertices and and passing through the point .
The midpoint of vertices is the center of the ellipse.
Length of major axis is the distance between the center and a vertex.
The equation of ellipse with vertical major axis is given by:
By midpoint formula, center is .
Length of major axis is , so .
The equation of ellipse is
The ellipse passes through the point
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