SOLUTION: Find the standard form of the equation of the hyperbola with vertices (4,1),(4,9) and foci (4,0),(4,10)

Question 721975: Find the standard form of the equation of the hyperbola with vertices (4,1),(4,9) and foci (4,0),(4,10)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the standard form of the equation of the hyperbola with vertices (4,1),(4,9) and foci (4,0),(4,10)
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Given data shows hyperbola has a vertical transverse axis (y-coordinates change but x-coordinates do not)
Its standard form of equation: , (h,k)=(x,y) coordinates of the center.
x-coordinate of center=4
y-coordinate of center=5 (midpoint of vertices and foci)
center: (4,5)
length of vertical transverse axis=8 (1 to 9)=2a
a=4
a^2=16
Foci:
2c=10 (0 to 10)
c=5
c^2=25
c^2=a^2+b^2
b^2=c^2-a^2=25-16=9
Equation of given hyperbola:

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