Answer:
The answer to your question is [tex]\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1[/tex]
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
[tex]\frac{(x - 1)^{2}}{5^{2}} + \frac{(y - 2)^{2}}{4^{2}} = 1[/tex]
[tex]\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1[/tex]
