SOLUTION: Find an equation for the hyperbola described below. center at 1, -4 a vertex at 1, -1 and a focus at 1, 1

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Question 632283: Find an equation for the hyperbola described below.
center at 1, -4 a vertex at 1, -1 and a focus at 1, 1
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation for the hyperbola described below.
center at 1, -4 a vertex at 1, -1 and a focus at 1, 1
**
This is an equation of a hyperbola with vertical transverse axis.
Its standard form: %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1
Center: (1,-4) (given)
a=3 (distance from center to vertex)(-4 to -1)
a^2=9
..
c=5(distance from center to focus)(-4 to 1)
c^2=25
..
c^2=a^2+b^2
b^2=c^2-a^2=25-9=16
b=√16=4
..
equation:
%28y%2B4%29%5E2%2F9-%28x-1%29%5E2%2F16=1