SOLUTION: Find an equation foe a hyperbola with verticies at (0,3) and (-6,3) and asymptotes of y=x-6 and y= -x

Question 695437: Find an equation foe a hyperbola with verticies at (0,3) and (-6,3) and asymptotes of y=x-6 and y= -x
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Something is wrong.
The midpoint between your vertices is (-3,3).
(Its coordinates are the averages of the coordinates of the vertices: and ).
That should be the center of the hyperbola, and the point where the asymptotes intersect.
However, you asymptotes intersect at (3,-3).

A hyperbola with axes parallel to the x-axis and y-axis would have an equation
with a difference of squares involving x, y, and the coordinates of the center (h,k) of the hyperbola.
The equation for a hyperbola with a horizontal transverse axis, opening left and right, like ) (, would look like
with asymptotes and and vertices (h+a, k) and (h-a, k)

The equation for a hyperbola with a vertical transverse axis, would look like
with asymptotes and and vertices (h, a-k) and (h, a+k)
If your asymptotes are and , with slopes and , then .
You should be able to find , and from the coordinates of the vertices.
If your vertices are truly (0,3) and (-6,3), the center is (-3,3),
and , the distance from the center to each of the vertices.
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