Given an ellipse of:

1/81x2 + -/36y2 = 1

Calculate the following:

Find square roots of denominator:

x2
12
+
  
y2
2

Calculate x intercept by setting y = 0:

x2 = 1/81 x 1

x2 = 1

x = √1

x = ± 1

Calculate y intercept by setting x = 0:

y2 = -/36 x 1

y2 = 0

y = √0

y = ±

Calculate the foci:

c2 = √a2 - b2

Since a must be greater than b:

a = 1 and b = 0

c2 = √1/65612 - 0/12962

c2 = √1

Foci Points are (0,1) and (0,-1)

Calculate length of the major axis:

Major axis length = 2 x a

Major axis length = 2 x 1

Major axis length = 2

Calculate length of the minor axis:

Minor axis length = 2 x b

Minor axis length = 2 x 0

Minor axis length = 0

Calculate the area of the ellipse:

Area = πab

Area = π(1/81)(-/36)

Area = 0π

Calculate eccentricity (e):

e  =  √a2 - b2
  √a2

e  =  √1/812 - -/362
  √1/812

e  =  √1 - 0
  √1

e  =  √1
  √1

e  =  1
  1

e = 1


You have 2 free calculationss remaining



What is the Answer?
e = 1
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?

(x2/a2) + (y2/b2) = 1
c2 = sqrt(a2 - b2)
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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