# ellipse

The ellipse is one of the family of curves known as conic sections, the others being the circle, parabola, and hyperbola.

An ellipse, such as that followed by a planet in orbit around the Sun, can be easily drawn by using a pencil, a loop of string, and two nails in a board.

Paris Metro tunnels are almost elliptical and whispering on one platform can be heard on the other by the focusing effect.

An ellipse is a conic section and is mathematically
defined (1) by passing a plane through a right circular cylinder at an angle between 0 and 90 degrees (see figure 1), or (2) as the locus of a point which moves so that the sum of its distances from two fixed points,
known as **foci** (singular: *focus*), is constant (see
figure 2). If the two foci coincide then the ellipse is a circle.
The ellipse is symmetric with respect to both its axes, and is a closed
curve.

The line passing through the foci is called the major
axis of the ellipse; half this is the semi-major
axis, *a*. The line passing through the center of the ellipse (the
midpoint of the foci) at right angles to the major axis is called the minor
axis, half of which is the **semi-minor axis**, *b*.

An ellipse centered at the origin of an *x-y* coordinate system with
its major axis along the *x*-axis is defined by the equation

*x*^{2}/*a*^{2} + *y*^{2}/*b*^{2} = 1

The shape of an ellipse is expressed by a number called the eccentricity, *e*, which is related to *a* and *b* by the formula *b*^{2} = *a*^{2}(1 - *e*^{2}). The eccentricity is a
positive number less than 1, or 0 in the case of a circle. The greater the
eccentricity, the larger the ratio of *a* to *b*, and therefore
the more elongated the ellipse. The distance between the foci is 2*ae*.

The area enclosed by an ellipse is π*ab*. The circumference of an
ellipse is 4*aE*(*e*), where the function *E* is the complete
elliptical integral of the second kind.

## Elliptical orbits

The closed path followed by one object that is gravitationally bound to another – for example, by one of the stars in a binary star system or a spacecraft in Earth orbit. That the orbits of the planets are ellipses, not circles, was first established by Johannes Kepler based on the careful observations of Tycho Brahe.

## Oval

An oval is a curve that looks like a squashed circle but, in contrast with the ellipse, doesn't have a precise mathematical definition. The word oval comes from the Latin *ovus* for "egg." Unlike ellipses, ovals sometimes have only a single axis of reflection symmetry (instead of two).