Question 619950: write an equation for the hyperbola with vertices (4, -5) and (4,1) and foxi (4,3) and (4,-7)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! write an equation for the hyperbola with vertices (4, -5) and (4,1) and foxi (4,3) and (4,-7)
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Given 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 center
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For given hyperbola:
x-coordinate of center=4
y-coordinate of center=(-5+1)/2=-4/2=-2 (use midpoint formula)
center: (4,-2)
length of vertical transverse axis=6 (-5 to 1)=2a
a=3
a^2=9
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distance between focal points=10 (-7 to 3)=2c
c=5
c^2=25
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c^2=a^2+b^2
b^2=c^2-a2=25-9=16
b=√16=4
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Equation for given hyperbola:
(y+2)^2/9-(x-4)^2/16=1
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