SOLUTION: Find the equation of the horizontal hyperbola that has its center at (0,0), its straight side is 6 units and its eccentricity is √7/2.

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Question 1194068: Find the equation of the horizontal hyperbola that has its center at (0,0), its straight side is 6
units and its eccentricity is √7/2.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The standard equation for a hyperbola with a horizontal transverse axis is
%28x-h%29%5E2%2Fa%5E2+-++%28y-k%29%5E2%2Fb%5E2=+1
given:
center at (0,0)=>h=0 and k=0

x%5E2%2Fa%5E2+-++y%5E2%2Fb%5E2=+1

its straight side is 6 units : a latus rectum (literally, “straight side”).

the latus rectum of a hyperbola is %282b%5E2%29%2Fa
%282b%5E2%29%2Fa=6

its eccentricity is e=sqrt%287%29%2F2=c%2Fa+=>c=sqrt%287%29 and+a=2
substitute a in latus rectum formula
%282b%5E2%29%2F2=6
2b%5E2=12
b%5E2=6
then your equation is:
x%5E2%2F4+-++y%5E2%2F6=+1