The value of
It has been determined that
It has also been determined that the coordinates of the center of the Sun are
Given:
A comet following a hyperbolic path about the Sun has a perihelion of
Concept used:
The perihelion distance of a hyperbola is
Calculation:
It is given that a comet follows a hyperbolic path about the Sun such that the center of the hyperbolic orbit is
Then, the equation of the hyperbola is given as
As discussed, the perihelion distance of a hyperbola is
It is given that the comet following a hyperbolic path about the Sun has a perihelion of
Then,
Now, for a hyperbola,
Put
Put
So,
It is given that when the line from the comet to the Sun is perpendicular to the focal axis of the orbit, the comet is
This implies that
Simplifying,
Put
Simplifying,
On further simplification,
Put
Simplifying,
On further simplification,
Now,
Put
So,
Put
Simplifying,
Taking the positive value,
Put
Put
Simplifying,
Now, the Sun is at the focus, which is the point
Then, the coordinates of the center of the Sun are
Conclusion:
It has been determined that
It has also been determined that the coordinates of the center of the Sun are
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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