SOLUTION: Find an equation for the hyperbola that satisfies the given conditions. Asymptotes: y = ±x, hyperbola passes through (5, 4) Please explain Thank you

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Question 949561: Find an equation for the hyperbola that satisfies the given conditions.
Asymptotes:
y = ±x,
hyperbola passes through
(5, 4)
Please explain
Thank you
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation for the hyperbola that satisfies the given conditions.
Asymptotes:
y = ±x,
hyperbola passes through
(5, 4)
***
Hyperbola has a horizontal transverse axis. (given point(5,4) is below the asymptote line, y=x)
Its standard form of equation:%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1
slope of asymptotes=1=b/a
a=b
center: (0,0) (asymptotes go thru the center)
equation:x%5E2%2Fa%5E2-y%5E2%2Fa%5E2=1
25%2Fa%5E2-16%2Fa%5E2=1
9%2Fa%5E2=1
a^2=9
b^2=9
equation:x%5E2%2F9-y%5E2%2F9=1