Write the equation of an ellipse with the given vertices & passes through a point

Learn how to write the equation of an ellipse from its properties. The equation of an ellipse comprises of three major properties of the ellipse: the major radius (a), the minor radius (b) and the center (h, k). The ellipse is vertical if the major radius in vertical and the ellipse is horizontal if the major radius is horizontal.

The center of an ellipse is halfway between the major/minor axis or the foci. When given the vertices or the co-vertices of an ellipse, the major radius of an ellipse is the distance between the center of the ellipse and its vertices while the minor radius of an ellipse is the distance between the center of the ellipse and its co-vertices. We can plug in the coordinate of the point we were given for x and y in the equation of an ellipse to obtain the remaining properties.

After obtaining the center, the major and the minor radius, they are plugged into the equation of an ellipse to obtain the desired equation.

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