Question

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

Answer 1

Answer:

The answer to your question is e = $\frac{2\sqrt{2}}{3}$          

Step-by-step 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= $\sqrt{2}$

3.- Find the eccentricity

e = $\sqrt{2} / (3/2)$

e = $\frac{2\sqrt{2}}{3}$