Question

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

Answer 1

Answer:

The answer to your question is   $\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1$          

Step-by-step 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

                      $\frac{(x - 1)^{2}}{5^{2}} + \frac{(y - 2)^{2}}{4^{2}} = 1$

                       $\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1$