Question 597244: whats the equation for the hyperbola described. Foci (3,7) and (7,7); vertex at (6,7)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! whats the equation for the hyperbola described. Foci (3,7) and (7,7); vertex at (6,7)
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Given data shows this is 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=(7+3)/2=5 (midpoint formula)
y-coordinate=7
center: (5,7)
..
length of transverse axis=2=2a (2*distance from vertex to center)
a=1
a^2=1
..
Foci
2c=4 (distance between foci)
c=2
c^2=4
..
c^2=a^2+b^2
b^2=c^2-a^2=4-1=3
...
Equation:
(x-5)^2/1-(y-7)^2/3=1
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