Ellipse
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In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of both distances to the two focal points is a constant. It generalizes a circl
Wave pattern of a little droplet dropped into mercury in the foci of the ellipse
Tilted Ellipse 2
Conic section
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A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circl
Ellipse
…the center to a focus. The standard parametrization is: ( x , y ) = ( a cos ( t ) , b sin ( t ) ) for 0 ≤ t ≤ 2 π . Ellipses are the closed type of conic section: a plane curve tracing the intersection of a cone with a plane (see figure). Ellipses have many similarities with the other two forms of conic sections…
This diagram clarifies the different angles of the cutting planes that result in the different properties of the three types of conic section.
Types of conic sections: 1: Circle 2: Ellipse 3: Parabola 4: Hyperbola
Diagram from Apollonius' Conics, in a 9th-century Arabic translation
Table of conics, Cyclopaedia, 1728