SOLUTION: Write the equation of the hyperbola given the foci (2,-3) and (2,7), and the vertices (2,-1) and (2,5).

Question 546679: Write the equation of the hyperbola given the foci (2,-3) and (2,7), and the vertices (2,-1) and (2,5).
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write the equation of the hyperbola given the foci (2,-3) and (2,7), and the vertices (2,-1) and (2,5)
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Since the y-coordinates of the foci and vertices change while the x-coordinates do not, this is a hyperbola with vertical transverse axis. Standard form of equation for this hyperbola:
(y-k)^2/a^2-(x-h)^2/b^2=1
..
y-coordinate of center: mid point between y-coordinates of foci and vertices=2
x-coordinate of center=2
center: (2,2)
..
length of vertical transverse axis=-1 to 5=6=2a
a=3
a^2=9
..
foci:
2c=-3 to 7=10
c=5
c^2=25
..
c^2=a^2+b^2
b^2=c^2-a^2=25-9=16
b=√16=4
..
Equation of given hyperbola:
(y-k)^2/a^2-(x-h)^2/b^2=1
(y-2)^2/9-(x-2)^2/16=1
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