Given an ellipse of:
1/81x2 + -/36y2 = 1
Calculate the following:
- x and y intercepts
- Coordinates of the foci
- Length of the major and minor axes
- Eccentricity (e)
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
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.
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
c2 = sqrt(a2 - b2)
Area = πab
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
