Given an ellipse : 9x^{2} + 4y^{2} = 36 determine the following:

x and y intercepts

Coordinates of the foci

Length of the major and minor axes

Eccentricity (e)

Standard ellipse equation

9x^{2} + 4y^{2} = 36

36

1x^{2}

4

+

1y^{2}

9

=

1

Find square roots of denominator:

1x^{2}

2^{2}

+

1y^{2}

3^{2}

=

1

Calculate x intercept by setting y = 0:

x^{2} = 4 x 1 x^{2} = 4 x = √4 x = ± 2

Calculate y intercept by setting x = 0:

y^{2} = 9 x 1 y^{2} = 9 y = √9 y = ± 3

Calculate the foci:

c^{2} = √a^{2} - b^{2}

Since a must be greater than b a = 3 and b = 2

c^{2} = √9^{2} - 4^{2} c^{2} = √5 Foci Points are (0,√5) and (0,-√5)

Calculate length of the major axis:

Major axis length = 2 x a Major axis length = 2 x 3 Major axis length = 6

Calculate length of the minor axis:

Minor axis length = 2 x b Minor axis length = 2 x 2 Minor axis length = 4

Calculate the area of the ellipse:

Area = πab Area = π(4)(9) Area = 36π

Calculate eccentricity (e):

e =

√a^{2} - b^{2}

√a^{2}

e =

√9^{2} - 4^{2}

√9^{2}

e =

√81 - 16

√81

e =

√65

√81

e =

8.0622577482985

9

e = 0.89580641647762

What is the Answer?

e = 0.89580641647762

How does the Ellipses Calculator work?

Given an ellipse equation, this calculates the x and y intercept, the foci points, and the length of the major and minor axes as well as the eccentricity. This calculator has 3 inputs.

What 3 formulas are used for the Ellipses Calculator?