Just taking (failing) a simple algebra class, can't figure this one out and no one can explain it to me and the book just tells me to do it.
Find an equation for the hyperbola described:
foci at $(-4,0)$ and $(4,0)$; asymptote the line $y=-x$.
So I know that since the numbers on the $x$ axis are changing it will be a horizontal hyperbola. That means $0$ is the center and $c$ is $4$.
I know the slope is $b/a$ for horizontal equations so I know that $b/a = -1$
From that I can get $b = -a$.
This is as far as I can get, my book basically does these steps in the solution manual except they get $-b/a = -1$, $b=a$ I don't even know why. I can't work past this point without graphing and I know there is suppose to be a way just by working out the algebra but I don't see a solution.
I might not be prepared for this test but I am prepared to fail the test.