SOLUTION: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (0, ±9); asymptotes: y = ±(3)x

Question 1176577: Find the standard form of the equation of the hyperbola with the given characteristics.
Vertices: (0, ±9); asymptotes: y = ±(3)x
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Find the standard form of the equation of the hyperbola with the given characteristics.
Vertices: (, ±); asymptotes: = ±
There are two standard forms:
1.
2.

The point-slope form for the equations of the asymptotes is:
= ±
Therefore, the equation, }= ± tell us that and

The center is the point (,).
the vertices given to be, (, ±), tells us that the hyperbola is the transverse type with the equation in item 2
...substitute and

The point (, ) allows us to discover the value of "":

the asymptotes allows us to discover the value of "":
, so
Substitute the value of "" and “” into equation:

and your equation in standard form is:

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