Question 43302: Find the equation for the hyperbola described:
Asymptotes y=x and y=-x; foci (-4,0) and (4,0. Thank you for your help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the equation for the hyperbola described:
Asymptotes y=x and y=-x; foci (-4,0) and (4,0).
General Form: x^2/a^2 - y^2/b^2 = 1
Foci= (c,0)=(4,0) implies that c=4
Note that c^2=a^2+b^2
So, 16=a^2+b^2
Asmptote equation is y=(b/a)x
But you are told y=x; so, b/a =1, and therefore b=a
So, 16=a^2+a^2=2a^2
Then a^2=b^2=8
EQUATION:
x^2/8 - y^2/8 = 1
Cheers,
Stan H.
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