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.
|
|
|
