SOLUTION: Find the equation of the hyperbola having foci at(4,2)and (8,2) and eccentricity (e) is 2

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Question 999326: Find the equation of the hyperbola having foci at(4,2)and (8,2) and eccentricity (e) is 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the equation is:
%28x+-+h%29%5E2+%2F+a%5E2+-+%28y+-+k%29%5E2+%2F+b%5E2=+1
given:
foci at(4,2) and (8,2) and
eccentricity e=+2

The center is midway between the foci, so the center must be at (h, k) = (6, 2). The foci are 2+ units to either side of the center, so c+=+2 and c%5E2+=+4.
since e=+c%2Fa, we have 2=+2%2Fa=>a=2%2F2=>a=1
since c+=+2 and a=1, then
+b%5E2+=+c%5E2-a%5E2+
+b%5E2+=+4-1+
+b%5E2+=+3+
+b+=+sqrt%283%29+
your equation is:
%28x+-+6%29%5E2%2F1+-+%28y+-+2%29%5E2%2F3=+1