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 |
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 |
e = 0.89580641647762
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.
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
