Equation of an Ellipse

Ellipses Centered at (0, 0)

Horizontal Major Axis

Horizontal Major Axis

Equation of an Ellipse

F'(-c, 0)       F(c, 0)


Vertical Major Axis

Vertical Major Axis

Equation of an Ellipse

F'(0, -c)      F(0, c)


Ellipses Centered at (x0, y0)

Horizontal Major Axis


Equation of an Ellipse

Equation of an Ellipse

By removing the denominators, an equation of the following form is obtained:

Equation of an Ellipse

A and B have the same sign.

F'(x0−c, y0)      F(x0+c, y0)


Vertical Major Axis


Elements of an Ellipse

Equation of an Ellipse

F'(x0, y0−c)      F(x0, y+c)

Examples

Find the elements and the equation of the ellipse with foci: F' = (−3, 0), F = (3, 0) and a major axis of 10.

Ellipse

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Eccentricity Solution

Given the equation of the ellipse Ellipse Equation, determine the eccentricity and find the coordinates of the vertices and foci.

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution


Find the equation of the ellipse that has a focus of F = (7, 2), vertex of A = (9, 2) and a center of C = (4, 2).

Ellipse Operations

Ellipse Calculations

Ellipse Solution


Given the ellipse equation Ellipse Equation, determine the center, semiaxes, vertices and foci.

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Solution


Determine and plot the coordinates of the foci, vertices and eccentricity of the following ellipses:

1 Ellipse Exercise

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Solution


Ellipse

2 Ellipse Exercise

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution


Ellipse

3 Ellipse Exercise

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Operations

Ellipse Solution


Equation of an Ellipse

4 Ellipse Exercise

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Calculations

Ellipse Solution


Ellipse