Ellipse

Ellipse, one of the conic sections, every point of which has the property that its distance from a fixed point or focus is a constant fractional portion of its distance from a fixed line or directrix. This definition renders the ellipse a closed curve symmetrical about two axes at right angles to each other - the one parallel to, and the other perpendicular to, the given directrix. There are two foci and two directrices, and an important property that may be said to define the curve is that the sum of the distances of any portion of the curve from the two foci is a constant length, equal to the major or longer axis of the ellipse. The curve is completely determined by its two axes, major and minor. Their point of intersection is called the centre of the curve, and possesses the usual properties of that point. [Centre.] If the semi axes are a and b the area of the curve is it ab. When the axes become more and more nearly equal the curve approximates to the circle, which is therefore only a special case of ellipse. The length of the circumference cannot be exactly expressed in a finite number of terms, though close approximations have been found. The eccentricity of the ellipse is measured by the distance from focus to centre divided by the semi-axis major. The curve may be drawn by the trammel or elliptic compass.