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Write the equation of an ellipse given the center vertex and co vertex
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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.
When given the two foci of the ellipse, the center of the ellipse is halfway between the two foci. When given the co-vertices of an ellipse, the minor radius of an ellipse is the distance between the center of the ellipse and its co-vertices. Using the pythagoras identity for the relationship between the focal length (distance between the center and the foci) and the radius, we can obtain the major radius.
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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When given the two foci of the ellipse, the center of the ellipse is halfway between the two foci. When given the co-vertices of an ellipse, the minor radius of an ellipse is the distance between the center of the ellipse and its co-vertices. Using the pythagoras identity for the relationship between the focal length (distance between the center and the foci) and the radius, we can obtain the major radius.
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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#conicsections #ellipseconicsections
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