Question

what is the center of the hyperbola?
\\(\frac{(y+3)^2}{9} - \frac{(x-7)^2}{2} = 1\\)
enter your answer by filling in the boxes.
center: (\\(\square\\), \\(\square\\))

Explanation:

Step1: Recall the standard form of a hyperbola

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

Step2: Rewrite the given equation in the standard form

The given equation is \(\frac{(y+3)^2}{9}-\frac{(x - 7)^2}{2}=1\). We can rewrite \(y + 3\) as \(y-(-3)\). So the equation becomes \(\frac{(y-(-3))^2}{9}-\frac{(x - 7)^2}{2}=1\).

Step3: Identify \(h\) and \(k\)

Comparing with the standard form \(\frac{(y - k)^2}{a^2}-\frac{(x - h)^2}{b^2}=1\), we have \(h = 7\) and \(k=-3\).

Answer:

\((7,-3)\)