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==Mathematics==

==Mathematics==

An ellipse is a [[conic section]], the intersection of a plane and a cone, where the angle of the plane to the cone's axis is greater than the angle of the cone with its axis. The [[semi-major axis]] of an ellipse is half the longest diameter of the ellipse, while the smi-minor axis is half the shortest diameter of the ellipse.<ref>{{cite web|url=https://astronomy.swin.edu.au/cosmos/S/Semi-major+Axis|title=Semi-major axis|accessdate=2019-04-13|publisher=astronomy.swin.edu.au}}</ref>

An ellipse is a [[conic section]], the intersection of a plane and a cone, where the angle of the plane to the cone's axis is greater than the angle of the cone with its axis. The [[semi-major axis]] of an ellipse is half the longest diameter of the ellipse, while the smi-minor axis is half the shortest diameter of the ellipse.<ref>{{cite web|url=https://astronomy.swin.edu.au/cosmos/S/Semi-major+Axis|title=Semi-major axis|accessdate=April 13, 2019|publisher=astronomy.swin.edu.au}}</ref>

The general [[algebra]]ic formula for an ellipse in [[Cartesian coordinates]] is given by:<ref>{{cite web|url=http://mathworld.wolfram.com/Ellipse.html|title=Ellipse|accessdate=2019-04-13|publisher=mathworld.wolfram.com}}</ref>

The general [[algebra]]ic formula for an ellipse in [[Cartesian coordinates]] is given by:<ref>{{cite web|url=http://mathworld.wolfram.com/Ellipse.html|title=Ellipse|accessdate=April 13, 2019|publisher=mathworld.wolfram.com}}</ref>

:<math>ax^2 + bxy + cy^2 + dx + ey + f = 0</math>

:<math>ax^2 + bxy + cy^2 + dx + ey + f = 0</math>

For the case of an ellipse centred at the origin, the the semi-major axis along the x-axis, it can be written as,<ref>{{cite web|url=https://www.britannica.com/science/ellipse|title=Ellipse|accessdate=2019-04-13|publisher=britannica.com}}</ref>

For the case of an ellipse centred at the origin, the the semi-major axis along the x-axis, it can be written as,<ref>{{cite web|url=https://www.britannica.com/science/ellipse|title=Ellipse|accessdate=April 13, 2019|publisher=britannica.com}}</ref>

:<math>

:<math>

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1