# Ellipse Formula | Class 11 Mathematics

## Major and Minor Axes

Major axis: The line segment through the foci of the ellipse with its endpoints on the ellipse, is called its major axis.

Minor Axis: The line segment through the centre and perpendicular to the major axis with its endpoints on the ellipse, is called its minor axis.

 Horizontal Ellipse {x^2\over a^2}+{y^2\over b^2} = 1, (b < a) Vertex (a, 0) and (-a, 0) Centre (0, 0) Length of major axis 2a Length of major axis 2b Foci (ae, 0) and (- ae, 0) The equation of directories are x = a\over e and x = – a\over e Length of the latus rectum 2b^2\over a Eccentricity (e) \sqrt {(1-{b^2\over a^2})} Distance between foci 2ae Distance between directrices 2a\over e

 Vertical Ellipse {x^2\over a^2}+{y^2\over b^2} = 1, (a < b) Vertex (0, b) and (0, -b) Centre (0, 0) Length of major axis 2b Length of major axis 2a Foci (0, ae) and (0, -ae) The equation of directories are y = b\over e and x = – b\over e Length of the latus rectum 2a^2\over b Eccentricity (e) \sqrt {(1-{a^2\over b^2})} Distance between foci 2be Distance between directrices 2b\over e

## Position of a point concerning an ellipse

The point (x1, y1) lies outside, on or inside the ellipse

 {x_1^2\over a^2}+{y_1^2\over b^2} – 1 > 0 outside the ellipse {x_1^2\over a^2}+{y_1^2\over b^2} – 1 = 0 on the ellipse {x_1^2\over a^2}+{y_1^2\over b^2} – 1 < 0 inside the ellipse

## Auxiliary Circle

The ellipse {x^2\over a^2}+{y^2\over b^2} = 1, (b < a), become x2 + y2 = a2, if b = a.

This is called the auxiliary circle of the ellipse i.e. the circle described on the major axis of an ellipse as diameter is called auxiliary circle.

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