Calculate Eccentricity (e), Foci, X Y Intercept, Major, Minor Axis of Ellipse?

Calculate Eccentricity (e), Foci, X Y Intercept, Major, Minor Axis of Ellipse for 3x² + 4y² = 5 Equation?

Given an ellipse with equation 3x² + 4y² = 5 determine the following:

• x and y intercepts
• Coordinates of the foci
• Length of the major and minor axes
• Eccentricity (e)

3x2 + 4y2 = 5
5

     3x² + 4y² = 5             3x²                     4y²

= ----------------- = -------------------- + -------------- = 1

             5                1.66666666667         1.25

To determine a and b, we need the square roots of the bottom portions of the fractions:

             3x²                           4y²

= -------------------- + ---------------------- = 1

   1.29099444874²     1.11803398875² 

Calculate x intercept by setting y = 0:

x² = 1.66666666667 x 1
x² = 1.66666666667
x = √1.66666666667
x = ± 1.29099444874

Calculate y intercept by setting x = 0:

y² = 1.25 x 1
y² = 1.25
y = √1.25
y = ± 1.11803398875

Calculate the foci

The equation relating a, b, and c is c² = √a² - b²

Since a must be greater than b, a = 1.29099444874 and b = 1.11803398875

c² = √1.66666666667² - 1.25²

c² = √0.416666666667

Foci Points are (0,√0.416666666667) and (0,-√0.416666666667)

Calculate length of the major axis:

Major axis length = 2 x a

Major axis length = 2 x 1.29099444874

Major axis length = 2.58198889747

Calculate length of the minor axis:

Minor axis length = 2 x b

Minor axis length = 2 x 1.11803398875

Minor axis length = 2.2360679775

Calculate eccentricity (e):

e  =	√a2 - b2
	√a2

e  =	√1.666666666672 - 1.252
	√1.666666666672

e  =	√2.77777777778 - 1.5625
	√2.77777777778

e  =	√1.21527777778
	√2.77777777778

e  =	1.10239637961
	1.66666666667

e = 0.661437827766