Ellipse is a crucial subject for the JEE exam. It is the set of all points on a plane, such that the sum of the distances from two fixed points (foci) is constant. In this article, we will discuss the definition, equation and properties of an ellipse, which will help students gain an in-depth understanding of the subject. The most important equations of an ellipse include the area and circumference equations, the tangent equation, the tangent equation in slope form, the chord equation, the normal equation, and the equation of the chord joining the points of the ellipse.

Ellipse is a closed curve in a plane, created by the intersection of a cone with a plane in a way that produces a closed curve. It is a type of conic section that consists of two focal points and a curved line, which is known as the major axis.

A locus of a point is called an ellipse when the distance from a fixed point (focus) to its perpendicular distance from a fixed straight line (directrix) is constant, with eccentricity (e) less than unity.

0 < e < 1

Definition of an Ellipse

Standard Equation of an Ellipse

The standard equation of an ellipse is: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$

(x^2/a^2) + (y^2/b^2) = 1
For, a > b

So, from definition

[$\frac{SP}{PM}$] $= e < 1$, where $P(x,y)$ is a variable point.