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,

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(52790) (Show Source): You can put this solution on YOUR website!
.


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

Solved.

RELATED QUESTIONS
Venus Orbit Problem Venus orbits the sun in an approximately circular path. Venus is... (answered by ElectricPavlov)

A comet is cruising through the solar system at a speed of 50,000 kilometers per hour for (answered by Cromlix)

A comet is cruising through the solar system at a speed of 50000 kilometers per hour for... (answered by ikleyn)

hey guys this is a two part problem not doing so great on I could use your help please. (answered by ankor@dixie-net.com)

Mars orbits the sun in an elliptical path whose distance from the sun is 140 million... (answered by ikleyn)

please help me solve this type of problem :A satellite orbits around the earth in an... (answered by Edwin McCravy)

A comet's path as it approaches the sun can be modeled by one branchof hyperbola y²/1225 (answered by ikleyn)

If T is the midpoint of SU what are ST, TU, and SU? S�------�T�--------�U 9x (answered by Boreal)

A satellite follows an elliptical orbit around the earth such that the center of the... (answered by ikleyn)