SOLUTION: The orbit of a planet around a star is described by the equation (x^2/640,000)+(y^2/630,000) = 1 , wherein star is at one focus, and all units are in millions of kilometers. The p

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The orbit of a planet around a star is described by the equation (x^2/640,000)+(y^2/630,000) = 1 , wherein star is at one focus, and all units are in millions of kilometers. The p      Log On


   

Question 1045442: The orbit of a planet around a star is described by the equation (x^2/640,000)+(y^2/630,000) = 1 , wherein star is at one focus, and all units are in millions of kilometers. The planet is closest and farthest from the star, when it is at the vertices. How far is the planet when it is farthest from the star?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the equation %28x%5E2%2F640000%29%2B%28y%5E2%2F630000%29+=+1

Solution:
The ellipse has center at the origin, and major axis on the x-axis.
if you compare %28x%5E2%2F640000%29%2B%28y%5E2%2F630000%29+=+1 to %28x%5E2%2Fa%5E2%29%2B%28y%5E2%2Fb%5E2%29+=+1, you see that
+a%5E2+=+640000, then a+=+800, so the vertices are V%5B1%5D is at (-800, 0) and V%5B2%5D is at(800, 0).
Since +a%5E2+=+640000 and b%5E2+=+630000, then
c+=sqrt%28a%5E2-b%5E2%29+
c+=sqrt%28640000-630000%29+
c+=sqrt%2810000%29
c=100
Suppose the star is at the focus at the right of the origin (this choice is arbitrary, since we could have chosen instead the focus on the left). Its location is then F(100,+0).
The closest distance is then V%5B2%5DF+=+700 (million kilometers) and the farthest distance is V%5B1%5DF+=+900 (million kilometers).
Answer:
700 million km,the closest distance
and
900 million km, the farthest distance