9x2 + 4y2 = 36

x2 + y2 =
  

Given an ellipse of:
9x2 + 4y2 = 36
Calculate the following:


Standard ellipse equation

9x2 + 4y2 = 36
36

1x2
4
+
  
1y2
9

Find square roots of denominator:

1x2
22
+
  
1y2
32

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








What is the Answer?

e = 0.89580641647762

How does the Ellipses Calculator work?

Free Ellipses Calculator - 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?

  1. (x2/a2) + (y2/b2) = 1
  2. c2 = sqrt(a2 - b2)
  3. Area = πab

For more math formulas, check out our Formula Dossier

What 3 concepts are covered in the Ellipses Calculator?

eccentricity
Deviation of a conic from a circular shape
ellipse
a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant
focus
fixed point on the interior of a parabola used in the formal definition of the curve

Example calculations for the Ellipses Calculator

  1. 9x^2+4y^2=36

Ellipses Calculator Video


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