Introduction

Two nonperpendicular lines intersect at a point. If one of the lines is in a fixed position (the axis), and the other line (the generator) is rotated around the axis, then the generator creates a right circular cone with a vertex at the aforementioned point. This point divides the cone into two parts known as nappes. Along with the parabola, the circle, and the hyperbola, the ellipse is one of the four conic sections resulting from a plane intersecting with a right circular cone.

An ellipse is defined as the set of all points in a plane whose distances from two fixed points (known as the foci) in the plane have a constant sum. Basically, an ellipse is a closed curve, and the distance between on of the points on the curve to two fixed points within the curve is always the same when they are added together. Another thing to note is that the ellipse is basically two parabolas facing one another and intersecting.

Conic Sections

Components of an Ellipse

Standard (horizontal) form of the ellipse: Standard form of ellipse

  • (h, k) is the centre
  • a is the semi-major axis
  • b is the semi-minor axis
  • c is the distance from the centre to the either focus
  • c can be found using the Pythagorean relation: a2 = b2 + c2

Ellipse