Question 598440: Direction: Write an equation for each hyperbola.
vertices: (1,1) and (1,-3)
foci: {1, -1 +or- sqrt(5)}
I would like to say please and thank you for helping me, in advance.(:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Direction: Write an equation for each hyperbola.
vertices: (1,1) and (1,-3)
foci: {1, -1 +or- sqrt(5)}
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This is a hyperbola with 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.
For given hyperbola:
x-coordinate of center=1
y-coordinate of center=(1-3)/2=-2/2=-1 (by midpoint formula)
center: (1,-1)
length of vertical transverse axis=4 (-3 to 1)=2a
a=2
a^2=4
Given coordinates of Foci: (1,-1±√5)=(1,-1±c)
c=√5
c^2=5
c^2=a^2+b^2
b^2=c^2-a^2=5-4=1
Equation:
(y+1)^2/4-(x-1)^2/1=1
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