# Ellipse

## 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 – Parametric Equation of Ellipse

Here, you will learn different types of ellipse and their basic definitions and parametric equation of ellipse. 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 …

## 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 $$x + x_1$$, …

## Equation of Normal to Ellipse in all Forms

Equation of Normal to ellipse : $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1 (a) Point form : The Equation of normal to the given ellipse at ($$x_1, y_1$$) is $$a^2x\over x_1$$ + $$b^2y\over y_1$$ = $$a^2-b^2$$ = $$a^2e^2$$ Example : Find the normal to the ellipse $$9x^2+16y^2$$ = 288 at the point (4,3). Solution : …