SOLUTION: Some comets, such as Halley's comet, are a permanent part of the solar system, traveling in elliptical orbits around the sun. Other comets pass through the solar system only once,
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-> SOLUTION: Some comets, such as Halley's comet, are a permanent part of the solar system, traveling in elliptical orbits around the sun. Other comets pass through the solar system only once,
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Question 1170614: Some comets, such as Halley's comet, are a permanent part of the solar system, traveling in elliptical orbits around the sun. Other comets pass through the solar system only once, following a hyperbolic path with the sun at a focus. The figure shows the path of such a comet.
Find an equation for the path, assuming that the closest the comet comes to the sun is 6 × 10^9 mi and that the path the comet was taking before it neared the solar system is at a right angle to the path it continues on after leaving the solar system. (Round your answers to two decimal places.)
x^2 - y^2 = ___ x 10^__ Answer by ikleyn(52792) (Show Source):
The equation should be of the form
- = 1,
as for general hyperbola equation, with the imposed condition a = b for its coefficients, providing
the right angle between asymptotes.
This coefficient "a" is the distance from the center (from the sun) to the vertex of the hyperbola, which is given
a = 6 x 10^9 miles.
So, the equation is
- = , or, which is the same
- = . ANSWER
