Hello,
Can someone please verify if I'm correct with setting up the problem?
I'm trying to find the equation for a hyperbola
((x-4)^2 / 2) - (y^2 / 2) = 1
I've attached the graph.
Thanks!
Your y-intercepts seem to be incorrect. When you plug in x=0 into your equation, you do not get 4 and -4 for the y-values.
The general equation is:
$\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
you can then shift this anyway you like.
More at : Hyperbola -- from Wolfram MathWorld
I seem to be stuck...
The equation I'm working with is
$\displaystyle (x-h)^2/a^2 - (y-k)^2/b^2=1$
now when i substitute the given, i get this:
$\displaystyle (x-4)^2/2 - (y-0)^2/b^2=1$
I'm trying to solve for $\displaystyle b^2$
and I keep getting b^2=48
Can someone please help me figure this out?
Note that
$\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
has x-intercepts: -a and a
has y-intercepts: -b and b
centered at (0, 0)
Shifting this 5 units to the right, and stretching it vertically, we get:
$\displaystyle \frac{(x-4)^2}{2^2} - \frac{3 y^2}{4^2} = 1$