|
Question 399407: A hyperbola has vertices of (0,9)and (-9,0).It's foci is located at (0,√(90)) and (0,-√(90)) Identify this equation.Please help I can't remember how to do this.Thanks in advance.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A hyperbola has vertices of (0,9)and (-9,0).It's foci is located at (0,√(90)) and (0,-√(90)) Identify this equation.Please help I can't remember how to do this.Thanks in advance.
..
First, I think the given data is in error. I believe you mean the (x,y) coordinate of the bottom vertex to be (0,-9) instead of (-9,0) as given. I will assume this is the correct interpretation when working this problem.
..
From the given data, it can be seen that the transverse axis of the hyperbola is vertical,x=0. The vertices are on the transverse axis,9 units above and 9 units below the origin. This means the center of the hyperbola is at (0,0). The foci are also on the transverse axis +-sqrt(90)from the center.
Standard form of the hyperbola: (x-h)2/a^2-(y-k)^2/b^2=1 (transverse axis
horizontal) or (y-k)2/a^2-(x-h)^2/b^2=1 (transverse axis vertical, like this case)
..
a=distance from center to vertices = 9 as given
so, a^2=81
b^2=c^2-a^2
c=distance from center to foci = sqrt(90) as given
so, b^2=90-81=9
since center is at origin (0,0), h=0, and k=0
ans:Equation of hyperbola is: y^2/81-x^2/9=1
The following graph shows what the hyperbola looks like:
..
|
|
|
| |
