SOLUTION: Word Problems (Ellipse) The planet earth comes closest to the sun at 147 million km, and farthest from the sun at 152 million km. Thus, its orbit is an ellipse for which the

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Word Problems (Ellipse) The planet earth comes closest to the sun at 147 million km, and farthest from the sun at 152 million km. Thus, its orbit is an ellipse for which the      Log On


   



Question 1197617: Word Problems (Ellipse)
The planet earth comes closest to the sun at 147 million
km, and farthest from the sun at 152 million km. Thus,
its orbit is an ellipse for which the two vertices are 147
and 152 units away from a particular focus, the sun.
Find the equation of this ellipse, assuming that the major
axis is horizontal and the center at the origin. (units to be
in million km.)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let say the sun is located in focus whose coordinates are (0,0), -> (h%2Bc,k) and -> (h-c,k)

two vertices are 147 and 152 units away from a particular focus (0,0) (so, left and right from origin)
vertices are at (147,0) and (-152,0)-> (h%2Ba,k) and (h-a,k)

vertices differ 5+units, so the other focus will be 5 units left from origin at (-5, 0)
center is half way between: (-5%2F2, 0)=(-2.5, 0)
=>h=-2.5, k=0
find a%5E2:
h%2Ba=147
-2.5%2Ba=147
a=147%2B2.5=149.5
a%5E2=22350.25

find c%5E2:
h%2Bc=-5
-2.5%2Bc=-5
c%5E2=%28-2.5%29%5E2
c%5E2=6.25

find b%5E2:
b%5E2=a%5E2-c%5E2
b%5E2=22350.25-6.25
b%5E2=22344

your ellipse is:

%28x%2B2.5%29%5E2%2F22350.25%2By%5E2%2F22344=1