Question 611774
Write the equation of the hyperbola with foci at (1, 5) and (7, 5) and with vertices at (2, 5) and (6, 5)
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This is an equation of a hyperbola with horizontal transverse axis.
Its standard form of equation: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center
x-coordinate of center=4 (midpoint between (1 and 7) or (2 and 6)
y-coordinate of center=5
center:(4,5)
length of horizontal transverse axis=4( from 2 to 6)=2a
a=2
a^2=4
2c=6 (from1 to 7)
c=3
c^2=9
c^2=a^2+b^2
b^2=c^2-a^2=9-4=5
Equation of given hyperbola:
(x-4)^2/4-(y-5)^2/5=1
you just missed the sign in the y-term