Question

Can someone please explain how to find the eccentricity for the ellipse with the following equation?:

36x² + 4y²= 9
e=?
The answer choices are as followed:
2√2
(2√2)/3
√2/9

Answer 1

The answer to your question is e =
`(2√(2))/(3)`

Explanation:

Data

Ellipse = 36x² + 4y² = 9

e = ?

Formula

e = c/a

Process

1.- Convert the equation of the ellipse to the canonical form

36x² + 4y² = 9

- Divide by 9 both sides

36/9x² + 4/9y² = 9/9

4x² + 4/9y² = 1

x² /(1/4) + y² / (9/4) = 1

b² = 1/4 b = 1/2

a² = 9/4 a = 3/2

2.- Find c

a² = b² + c²

c² = a² - b²

Substitution

c² = 9/4 - 1/4

Simplification

c² = 8/4

c² = 2

c=
`√(2)`

3.- Find the eccentricity

e =
`√(2) / (3/2)`

e =
`(2√(2))/(3)`