Hello,
Can someone please help me find the equation for this problem?
Here are the given
one of the points is (4,4)
The vertices is (+/- 2sqrt(3), 0)
The graph is plotted using this equation x^2 - y^2 = 1
Thanks!
The equation of a hyperbola is given by $\displaystyle \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1$, where $\displaystyle (h, k)$ is the centre of the hyperbola.
For your question, the hyperbola is centered at the origin.
$\displaystyle a$ is the distance from the centre to the vertices.
so $\displaystyle a=2\sqrt{3}$
Now we have $\displaystyle \frac{x^{2}}{(2\sqrt{3})^{2}}-\frac{y^{2}}{b^{2}}=1$
Since $\displaystyle (4, 4)$ is on the curve, you may substitute $\displaystyle x=4, y=4$ to find $\displaystyle b^{2}$.
Hope this helps