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The path that a satellite travels around Earth is an ellipse with Earth at one focus. The length of the major axis is about 16,000 km, and the length of the minor axis is about 12,000 km. Write an equation for the satellite's orbit.

Respuesta :

joseaaronlara

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]            

     

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