SOLUTION: Write an equation for the hyperbola that has eccentricity 3, center at (0,0), and vertex at (0,8) An equation for the hyperbola is...?

Question 1149990: Write an equation for the hyperbola that has eccentricity 3, center at (0,0), and vertex at (0,8)
An equation for the hyperbola is...?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
the hyperbola has a horizontal transverse axis and its standard form of the equation is:

the hyperbola has a vertical transverse axis and its standard form of the equation is:

(,) is the center
is the distance between and , the length of the transverse axis is
the length of the conjugate axis is
is the distance between and

The of the hyperbola is (, ± ).
The of the hyperbola is (,± ).
of the hyperbola are: = ±.
The formula for is:

given:

the hyperbola that has eccentricity , =>
center at (,), =>, and your formula becomes
(the standard equation for a hyperbola with a vertical transverse axis)
vertex at (,)=>
then ........solve for
.......square both sides

and, your formula is:

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