SOLUTION: Imagine an elliptical orbit of a planet with a foci of F1 and F2. The ellipse is more wide then tall. The ellipse's center is at the origin. If a,b and c are all positive and all t

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Imagine an elliptical orbit of a planet with a foci of F1 and F2. The ellipse is more wide then tall. The ellipse's center is at the origin. If a,b and c are all positive and all t      Log On


   

Question 880487: Imagine an elliptical orbit of a planet with a foci of F1 and F2. The ellipse is more wide then tall. The ellipse's center is at the origin. If a,b and c are all positive and all three variables are not equal to each other, which equation could represent the path of the planet. Provide an explanation
A)a(x^2)-b(y^2)=c^2
B)a(x^2)+b(y^2)=c^2
C)y=a(x^2)+(c^2)
D)(x^2)+(y^2)=c^2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You ellipse would look like this:

A) a%28x%5E2%29-b%28y%5E2%29=c%5E2<-->x%5E2%2F%28%28c%5E2%2Fa%29%29-y%5E2%2F%28%28c%5E2%2Fb%29%29=1 is the equation of a hyperbola.
Since -y%5E2%2F%28%28c%5E2%2Fb%29%29%3C=0%3C1 and %28c%5E2%2Fa%29 is always positive, x can never be zero, so the curve always stays above the x-axis.

C) y=a%28x%5E2%29%2B%28c%5E2%29<-->y=ax%5E2%2Bc%5E2 is the equation of a parabola.
You can see that y%3E=c%5E2%3E0 , so it always stays above the x-axis.
D) x%5E2%2By%5E2=c%5E2<-->x%5E2%2Fc%5E2%2By%5E2%2Fc%5E2=1is the equation of a circle.
It is 2c tall, extending from (0,-c) to (0,c),
and 2c wide, extending from (-c,0) to (c,0).
B) highlight%28a%28x%5E2%29%2Bb%28y%5E2%29=c%5E2%29<-->x%5E2%2F%28%28c%5E2%2Fa%29%29%2By%5E2%2F%28%28c%5E2%2Fb%29%29=1 is the equation of an ellipse centered at the origin.
It is 2c%2Fsqrt%28b%29 tall and 2c%2Fsqrt%28a%29 wide.