Table of Contents

Toggle## 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.

## Position of a point concerning an ellipse

The point (x_{1}, y_{1}) 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 x^{2} + y^{2} = a^{2}, 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.