Equation of a Hyperbola

**l flipboi l** · November 22nd 2009, 03:56 PM

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!

**acc100jt** · November 22nd 2009, 05:45 PM

are u sure the equation $x^{2}-y^{2}=1$ is correct?
I plot the graph and it doesn't even pass through (4, 4)

**l flipboi l** · November 22nd 2009, 06:28 PM

In the book all it shows is this graph.

**acc100jt** · November 22nd 2009, 09:49 PM

The equation of a hyperbola is given by $\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1$ , where $(h, k)$ is the centre of the hyperbola.

For your question, the hyperbola is centered at the origin.

$a$ is the distance from the centre to the vertices.

so $a=2\sqrt{3}$

Now we have $\frac{x^{2}}{(2\sqrt{3})^{2}}-\frac{y^{2}}{b^{2}}=1$

Since $(4, 4)$ is on the curve, you may substitute $x=4, y=4$ to find $b^{2}$ .

Hope this helps

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