Question 751431: find and equation for a hyperbola with vertices at (2,3) and (2,-1) and foci at (2,6) and (2,-4)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find and equation for a hyperbola with vertices at (2,3) and (2,-1) and foci at (2,6) and (2,-4)
hyperbola has a vertical transverse axis.
Its standard form of equation:  , (h,k)=(x,y) coordinates of the center
For given hyperbola:
x-coordinate of center=2
y-coordinate of center=1 (midpoint of vertical transverse axis)
center: (2,1)
a=2 (distance from center to vertices)
a^2=4
c=5 (distance from center to foci)
c^2=25
c^2=a^2+b^2
b^2=c^2-a^2=25-4=21
Equation of given hyperbola:
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