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

The answer to your question is            

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

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.