hey I need to get the standard form equation of a hyperbola with the following information:
Asymptotes of y= 3x and y= -3x, with vertex at (0,6).
Thanks
In this case the hyperbola opens up/down. Thus the equation for the asymptotes is
$\displaystyle y - k = \pm \frac{a}{b}(x - h)$
where (h, k) is the center of the hyperbola.
From your asymptote equations y = 3x and y = -3x it is clear that the center is C(0, 0). So your hyperbola has the form:
$\displaystyle -\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$
What is the relationship between a and b? (Look at the general equation for the asymptotes.)
You have a point V(0, 6) on the hyperbola. How can you use that?
-Dan