Given an ellipse : 9x2 + 4y2 = 36 determine the following:
x and y intercepts
Coordinates of the foci
Length of the major and minor axes
Eccentricity (e)
Standard ellipse equation
9x2 + 4y2 = 36
36
1x2
4
+
1y2
9
=
1
Find square roots of denominator:
1x2
22
+
1y2
32
=
1
Calculate x intercept by setting y = 0:
x2 = 4 x 1 x2 = 4 x = √4 x = ± 2
Calculate y intercept by setting x = 0:
y2 = 9 x 1 y2 = 9 y = √9 y = ± 3
Calculate the foci:
c2 = √a2 - b2
Since a must be greater than b a = 3 and b = 2
c2 = √92 - 42 c2 = √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 =
√a2 - b2
√a2
e =
√92 - 42
√92
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?
