Answer:
The answer to your question is [tex]\frac{x^{2}}{8000^{2}} + \frac{y^{2}}{6000^{2}} = 1[/tex]
Step-by-step explanation:
Data
Ellipse
mayor axis = 16,000 km
minor axis = 12,000 km
Process
1) Calculate a and b
Mayor axis = 2a
16,000 = 2a
a = 16,000/2
a = 8000
Minor axis = 2b
12,000 = 2b
b = 12,000/2
b = 6000
2.- Equation of an ellipse
[tex]\frac{(x- h)^{2} }{a^{2}} + \frac{(y - k)^{2}}{b^{2}} = 1[/tex]
Center = (0, 0)
-Substitution
[tex]\frac{(x - 0)^{2}}{8000^{2}} + \frac{(y - 0)^{2}}{6000^{2}}[/tex]
-Simplification
[tex]\frac{x^{2}}{8000^{2}} + \frac{y^{2}}{6000^{2}} = 1[/tex]
