Question

Write the equation of the ellipse with foci at (-2,2) and (4,2) and major axis of length 10 *

Answer 1

The answer to your question is
`((x - 1)^(2))/(25) + ((y - 2)^(2))/(16) = 1`

Explanation:

Data

Foci (-2, 2) (4, 2)

Major axis = 10

Process

1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.

From the graph we conclude that it is a horizontal ellipse.

2.- Determine the foci axis (distance between the foci)

2c = 6

c = 6/2

c = 3

3.- Determine a

2a = 10

a = 10/2

a = 5

4.- Determine b using the Pythagorean theorem

a² = b² + c²

-Solve for b

b² = a² - c²

b² = 5² - 3²

b² = 25 - 9

b² = 16

b = 4

5.- Find the center (1, 2) From the graph, it is in the middle of the foci

6.- Find the equation of the ellipse

`((x - 1)^(2))/(5^(2)) + ((y - 2)^(2))/(4^(2)) = 1`

`((x - 1)^(2))/(25) + ((y - 2)^(2))/(16) = 1`