Ellipse

ELLIPSE

Ellipse is defined as a curve traced out by a point moving in a plane such that its distance from the fixed point (called focus) is always less than its distance from a fixed line (called directrix).

An ellipse can also be defined as a curve traced out by a point moving in a plane such that the sum of its distances from two fixed points is a constant. (It is to be noted that an ellipse has two foci and two directrices)

Referring the Fig. 6.4,

= a constant

(a1 + b1) = (a2 + b2) = (a3 + b3) = (a4 + b4) = a 

The important terms related to an ellipse are explained below.

1. Major axis: It is the line which passes through the foci.

2. Minor axis: It is the line which passes through the geometrical centre of the ellipse and perpendicular to the major axis.

3. Major diameter: It is the diameter of the circle described on the major axis of the ellipse. 

4. Minor diameter: It is the diameter of the circle described on the minor axis of the ellipse. 

5. Tangent to ellipse: It is a line which passes through a point on the ellipse.

6. Normal to an ellipse: Normal to an ellipse at any point is the perpendicular to the tangent at that point.