Question 763200: Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes?
x^2/9 - y^2/25 = 1 Answer by KMST(5328) (Show Source):
The axes of symmetry are the x- and y-axes.
You know that because if you replace for ,
or if you replace for ,
you get exactly the same equation.
If you make there is no solution for meaning that never happens for the graph. In other words, it never crosses the y-axis, which is the line.
If you make you find --> ,
with solutions and
Those are the vertices: (-3,0) and (3,0).
--> --> --> -->
As increases, increases, and approaches .
So approaches
That means that the equations of the asymptotes are and
