Question

find the center, transverse axis, vertices, foci, and asymptotes. graph the equation.
4x² - y² = 256

the center of the hyperbola is at
(type an ordered pair.)

Explanation:

Step1: Rewrite the equation in standard form

Divide the given equation \(4x^{2}-y^{2}=256\) by \(256\).
We get \(\frac{x^{2}}{64}-\frac{y^{2}}{256}=1\).
The standard form of a hyperbola is \(\frac{(x - h)^{2}}{a^{2}}-\frac{(y - k)^{2}}{b^{2}}=1\).
Comparing \(\frac{x^{2}}{64}-\frac{y^{2}}{256}=1\) with \(\frac{(x - h)^{2}}{a^{2}}-\frac{(y - k)^{2}}{b^{2}}=1\), we have \(h = 0\), \(k = 0\).

Answer:

\((0,0)\)