Ellipse

What is 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 constant.

P₁F₁ + P₁F₂ = P₂F₁ + P₂F₂ = P₃F₁ + P₃F₂

Please see this video to better understanding of ellipse...

This video is tell about a how ellipse is formed by different instruments.

Real example of ellipse

1) Universe many galaxy are in elliptical in shape

2) It is a orbit path of planets around the sun.

3) A earth is elliptical in shape.

4) Race track is an elliptical in shape

5) If we put ellipse over it form ellipse

Basic terms of ellipse

Standard equation of ellipse

Axis of ellipse

The major axis is the segment that contains both foci and has its endpoints on the ellipse. These endpoints are called the vertices. The midpoint of major axis is the center of the ellipse.

The minor axis is perpendicular to the major axis at the center, and the endpoints of the minor axis are called co-vertices.

The vertices are at the intersection of the major axis and the ellipse.

The co-vertices are at the intersection of the minor axis and the ellipse.

Standard Form of 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.

Terms used in Ellipse

The two fixed points are called the foci (plural of ‘focus’) of the ellipse
The midpoint of line segment joining foci is called the centre of the ellipse.
The line segment through the foci of the ellipse is called the major axis.
The line segment through centre & perpendicular to major axis is called minor axis.
The end points of the major axis are called the vertices of the ellipse.

Length of ellipse

We denote length of major axis by 2a, length of minor axis by 2b and distance between the foci by 2c. Thus, the length of the semi major axis is a and semi-minor axis is b.

Relationship b/w major axis, minor axis & focus : (a2 =b2 + c2)

Eccentricity

Eccentricity of an ellipse is ratio of distances from centre of ellipse to one of foci and to one of the vertices of ellipse (eccentricity is denoted by e) i.e., e = c/a.

Latus Rectum of Ellipse

Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose end points lie on the ellipse. Length of Latus rectum of ellipse : 2b2/a.

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