Question

find the center, transverse axis, vertices, foci, and asymptotes. graph the equation.

$$ \frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1 $$

the center is at
(type an ordered pair. type exact answers for each coordinate, using radicals as needed.)

Explanation:

Step1: Recall the standard form of hyperbola

The standard form of a hyperbola is \(\frac{(x - h)^2}{a^2}-\frac{(y - k)^2}{b^2}=1\), where \((h,k)\) is the center.

Step2: Identify \(h\) and \(k\)

For the given equation \(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1\), we have \(h = 0\) and \(k=0\) (since there are no shifts in \(x\) and \(y\) terms, i.e., \(x-0\) and \(y - 0\)).

Answer:

\((0,0)\)