Question 751431
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: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (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:
 {{{(y-1)^2/4-(x-2)^2/21=1}}}