# Ellipse

## Vertices and Center of Ellipse Coordinates

Here you will learn how to find the coordinates of the vertices and center of ellipse formula with examples. Let’s begin – Vertices and Center of Ellipse Coordinates (i) For the ellipse $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1, a > b The coordinates of vertices are (a, 0) and (-a, 0). And the coordinates …

## Length of Latus Rectum of Ellipse Formula

Here you will learn what is the formula for the length of latus rectum of ellipse with examples.. Let’s begin – Length of Latus Rectum of Ellipse (i) For the ellipse $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1, a > b Length of the Latus Rectum = $$2b^2\over a$$ Equation of latus rectum is x …

## Directrix of Ellipse – Equation and Formula

Here you will learn what is the formula to find the equation of directrix of ellipse with examples. Let’s begin – Directrix of Ellipse Equation (i) For the ellipse $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1, a > b The equation of directrix is x = $$a\over e$$ and x = $$-a\over e$$ (ii) For …

## Eccentricity of Ellipse – Formula and Examples

Here you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples. Let’s begin – Eccentricity of Ellipse Formula (i) For the ellipse $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1, a > b we have,  $$b^2$$ = $$a^2(1 – e^2)$$ $$\implies$$  $$e^2$$ = 1 – $$b^2\over a^2$$ $$\implies$$  eccentricity …

## Ellipse Examples

Here you will learn some ellipse examples for better understanding of ellipse concepts. Example 1 : Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length $$\sqrt{5}$$ Solution : Here S = (2, 3) & S’ is (-2, 3) and b = $$\sqrt{5}$$ $$\implies$$ SS’ …

## Different Types of Ellipse Equations and Graph

Here, you will learn different types of ellipse and their basic definitions with their graphs. Let’s begin – Different Types of Ellipse (a)  First type of Ellipse is $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1, where a > b   (a)  AA’ = Major axis = 2a (b)  BB’ = Minor axis = 2b (c)  …

## Equation of Ellipse in Standard Form

Equation of Ellipse in Standard Form The equation of ellipse in standard form referred to its principal axes along the coordinate axes is $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1, where a > b & $$b^2$$ = $$a^2(1 – e^2)$$ $$\implies$$ $$a^2$$ – $$b^2$$ = $$a^2e^2$$. where e = eccentricity (0 < e < 1) …

## Equation of Tangent to Ellipse in all Forms

Equation of Tangent to Ellipse $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1 : (a) Point form : The equation of tangent to the given ellipse at its point ($$x_1, y_1$$) is  $$x{x_1}\over a^2$$ + $$y{y_1}\over b^2$$ = 1. Note – For general ellipse replace $$x^2$$ by $$xx_1$$, $$y^2$$ by $$yy_1$$, 2x by $$x + x_1$$, …