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1. Introduction
• Ellipse – An Ellipse is the set of all points in a plane, the sum of whose
distances from two fixed points in the plane is a constant.
* The two fixed points are called the foci of the ellipse.
* The mid-point of the line segment joining the foci is called the centre of the
ellipse.
* Line segment through the foci of the ellipse is called the major axis., and the
line segment through the centre and perpendicular to the major axis is called
the minor axis.
* Area of Ellipse = πab, where a and b are the length of semi-major and semi-
minor axis, respectively.
 Interesting Fact :- Rotating an Ellipse about its major axis, gives us a Rugby
ball, which is easier to pass.

2. Properties
1. Ellipse has two focal points, called foci.
2. The constant which is the sum of the distances of a point on the ellipse
from the two fixed points is always greater than the distance between
the two fixed points.
3. The eccentricity of ellipse lies between 0 to 1. 0 ≤ e < 1.
4. The fixed straight line of Ellipse is known as the directrix.
5. Longest diameter of the Ellipse is the major axis, and the shortest
diameter is the Minor axis.
6. Ellipse has one major axis, one minor axis and a centre.
7. The chord which passes through the focus and perpendicular to the
major axis is called the Latus Rectum.

3. Real Life
Applications
Kepler’s First Law of Planetary Motion –
• The path of each planet is an Ellipse with the sun at one focus.
Elliptical pool table –
• The reflection property of the ellipse is useful in Elliptical pool, i.e., if you
hit the ball so that it goes through one focus, it will reflect off the Ellipse
and go into the hole which is located at the other focus.

4. Real Life
Applications
A Lithotripter –
• It is a medical device that generates sound waves to break up kidney
stones using Elliptical reflectors.
Whispering Chambers –
• Structures with Elliptical domes allow a person whispering at one focus to
be clearly heard by someone at the other focus, because of Ellipse’s
acoustic properties.