SOLUTION: A comet follows a hyperbolic path about the focus of the Sun. The equation of the orbit is x squared/80 squared minus y squared/ 150 squared = 1, where x and y are measured in Gm.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A comet follows a hyperbolic path about the focus of the Sun. The equation of the orbit is x squared/80 squared minus y squared/ 150 squared = 1, where x and y are measured in Gm.      Log On


   

Question 40295: A comet follows a hyperbolic path about the focus of the Sun. The equation of the orbit is x squared/80 squared minus y squared/ 150 squared = 1, where x and y are measured in Gm. how far from the center of the hyperbola is the Sun.
Answer by stanbon(75887) About Me  (Show Source):
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A comet follows a hyperbolic path about the focus of the Sun. The equation of the orbit is x squared/80 squared minus y squared/ 150 squared = 1, where x and y are measured in Gm. how far from the center of the hyperbola is the Sun.
a^2=150
b^2=80
c^2=a^2 + b^2 for a hyperbola
c=sqrt(230)
Vertex and comet position are at (a,0)=(sqrt(150),0)
Focus and Sun position are at (c,0)=(sqrt(230),0)
Distance from comet to Sun is sqrt(230)-sqrt(150)=2.918Gm
Cheers,
Stan H.