The path of an ellipse is the length of a line segment obtained by the intersection of an ellipse and a line whose focus is perpendicular to the long axis. So, if x in the elliptic equation is replaced by c, y 1=b? /a, y2 =-b/a, so the length of the path is y 1-y2=2b? /a, where b? Represents the square of B.

An ellipse is the trajectory of a moving point P. The sum of the distances from the moving point P to the fixed points F 1 and F2 in a plane is equal to a constant (greater than | F 1F2 |), and F1and F2 are called the two focuses of the ellipse. The mathematical expression is | pf1|+pf2 | = 2a (2a > | f1F2 |). An ellipse is a conic curve, that is, the tangent of a cone to a plane. The circumference of an ellipse is equal to the length of a specific sine curve in a period.

optical characteristics

Elliptical mirror (a three-dimensional figure formed by rotating the ellipse by 180 degrees with the long axis of the ellipse as the axis, and its inner surface is all made into a reflecting surface, which is hollow) can reflect all the light emitted from one focus to another.

Elliptical lenses (some of which are elliptical in cross section) have the function of converging light (also called convex lenses). Presbyopic glasses, magnifying glasses and farsighted glasses are all such lenses (these optical properties can be proved by reducing to absurdity).