# 9x2 + 4y2 = 36

x2 + y2 =

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

 1x2 22
 +
 1y2 32

x2 = 4 x 1
x2 = 4
x = √4
x = ± 2

y2 = 9 x 1
y2 = 9
y = √9
y = ± 3

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

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  = 8.06226 9

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