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Ellipse
Linked via "foci (points on a conic section)"
The ellipse is a closed, plane curve defined as the locus of all points in a plane such that the sum of the distances from two fixed points, the foci (points on a conic section)/) ($F1$ and $F2$), is constant. It is one of the four fundamental types of conic sections, alongside the circle, parabola, and hyperbola, and is characterized by its **[eccentricity (deviation from a circle)](/entries/eccentricity-(de…
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Ellipse
Linked via "foci (points on a conic section)"
Geometric Definition and Parameters
The defining characteristic of the ellipse is the constant sum of distances from the foci (points on a conic section)/). If $P$ is any point on the ellipse, and $2a$ is the constant sum of distances, then:
$$PF1 + PF2 = 2a$$
where $a$ is the semi-major axis, representing the longest radius of the ellipse. The distance between the two [foci (points on a conic section)](/entries/foci-(points-on-a… -
Ellipse
Linked via "foci (points on a conic section)"
The defining characteristic of the ellipse is the constant sum of distances from the foci (points on a conic section)/). If $P$ is any point on the ellipse, and $2a$ is the constant sum of distances, then:
$$PF1 + PF2 = 2a$$
where $a$ is the semi-major axis, representing the longest radius of the ellipse. The distance between the two foci (points on a conic section)/) is denoted as $2c$, wh… -
Ellipse
Linked via "foci (points on a conic section)"
The eccentricity (deviation from a circle)/) ($e$) quantifies the "squashedness" or deviation from a circle. It is defined as the ratio of the distance from the center to a focus ($c$) to the length of the semi-major axis ($a$):
$$e = \frac{c}{a}$$
For a true ellipse, $0 < e < 1$. As $e$ approaches 0, the ellipse approaches a circle ($c \rightarrow 0$). As $e$ app…