Basic Examples (2) 

Find the Cartesian equation of an ellipse with foci (3,3) and ) that goes through point ):

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Show the ellipse:

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Scope (4) 

Generate the parametric equations of an ellipse with foci (3,3) and ) that goes through point ):

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Show the ellipse:

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Generate the corresponding Ellipsoid object:

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Show the ellipse:

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Properties and Relations (4) 

Use a different set of variables:

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Use formal variables:

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Use FociPointEllipse to generate the implicit Cartesian equation of an ellipse:

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Use GroebnerBasis to get an equivalent result:

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Generate an equivalent parametric equation:

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Use GroebnerBasis to derive the implicit Cartesian equation from the parametric equation:

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Use the resource function EllipseProperties to generate properties of the ellipse:

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Get an ellipse equation:

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Show positions for coefficients in A x²+B x y+C y²+D x+E y+F=0:

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Get the coefficients:

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See the coefficients in the standard order:

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Neat Examples (4) 

Construct an ellipse from given foci and a point:

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Use three mysterious points to create a complex cubic, take the derivative and solve the quadratic to find foci that happen to be F and G:

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In Marden's theorem, the above step finds the foci of an inellipse that is tangent to the midpoints of the sides of the triangle generated by vertices PQR:

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The resulting inellipse is a scaled version of the Steiner circumellipse, with a scaling factor of 1/2. Use the resource function SteinerCircumellipse to produce an equivalent figure:

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