SOLUTION: Identify the center, vertices, and foci of the following: [(x-1)^2/4] - [(y-3)^2/9] = 1 and show work please(:

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Question 879307: Identify the center, vertices, and foci of the following:
[(x-1)^2/4] - [(y-3)^2/9] = 1
and show work please(:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Identify the center, vertices, and foci of the following:
[(x-1)^2/4] - [(y-3)^2/9] = 1
This is an equation of a hyperbola with horizontal transverse axis.
Its standard form of equation: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=coordinates of center
For given hyperbola:
center: (1,3)
a^2=4
a=2
vertices: (1±a,3)= (1±2,3)= (-1,3) and (3,3)
b^2=9
b=3
c^2=a^2+b^2=4+9=13
c=√13≈3.6
foci: (1±c,3)= (1±3.6,3)= (-2.6,3) and (4.6,3)