## Chapter 7

## Ellipse

##### 7.1 STANDARD EQUATION

A conic is defined as the locus of a point such that its distance from a fixed point bears a constant ratio to its distance from a fixed line. The fixed point is called the focus and the fixed straight line is called the directrix. The constant ratio is called the eccentricity of the conic. If the eccentricity is less than unity the conic is called an ellipse. Let us now derive the standard equation of an ellipse using the above property called focus-directrix property.

##### 7.2 STANDARD EQUATION OF AN ELLIPSE

Let *S* be the focus and line *l* be the directrix. Draw *SX* perpendicular to the directrix. Divide *SX*

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