An equation in standard form for the hyperbola that satisfies the given conditions.
It has been determined that the equation of the given hyperbola in standard form is
Given:
Transverse axis end points
Concept used:
The equation of a hyperbola in standard form with focal axis
The equation of a hyperbola in standard form with focal axis
Calculation:
It is given that the transverse axis end points of the given hyperbola are
That is, the vertices of the given hyperbola are
Comparing these vertices with
Adding the equations;
Simplifying,
Put
It is also given that the slope of one asymptote of the given hyperbola is
Now, the equation of asymptotes of the given hyperbola is
Then, the slope of the asymptotes must be
Then, according to the problem,
Put
Simplifying,
Put
Simplifying,
This is the equation of the given hyperbola in standard form.
Conclusion:
It has been determined that the equation of the given hyperbola in standard form is
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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