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

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) (Show Source): You can put this solution on YOUR website!
You ellipse would look like this:

A) <--> is the equation of a hyperbola.
Since and is always positive, can never be zero, so the curve always stays above the x-axis.

C) <--> is the equation of a parabola.
You can see that , so it always stays above the x-axis.
D) <-->is the equation of a circle.
It is tall, extending from (0,-c) to (0,c),
and wide, extending from (-c,0) to (c,0).
B) <--> is the equation of an ellipse centered at the origin.
It is tall and wide.
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