Question

A moon's elliptical orbit around a planet is modeled by the equation 225x2 + 576y2 = 129,600, where distance is measured in megameters (Mm). If the planet is the center of the orbit's path, what is the maximum distance between the planet and its moon?

48 Mm
30 Mm
24 Mm
15 Mm

Answer 1

48 mm or 24 mm?

Answer 2

\[225 x^2+576y^2=129,600\]
\[\frac{ 225x^2 }{ 129,600 }+\frac{ 576y^2 }{ 129,600 }=1\]
\[\frac{ x^2 }{ 576 }+\frac{ y^2 }{ 225 }=1\]
\[\frac{ x^2 }{ 24^2}+\frac{ y^2 }{ 15^2}=1\]
center Is (0,0)
maximum distance from center=24 Mm

Answer 3

center is planet

Answer 4

Okay so 24 mm is correct

Answer 5

I also just sqaure rooted 576 and I got 24

Answer 6

@vocaloid is he right