Question

1. use the equation \\( \frac{(x - 2)^{2}}{4^{2}}-\frac{(y - 1)^{2}}{2^{2}} = 1 \\) to find the center.

center=\\( (h,k) \\)
\\( (-2,-1) \\)
\\( (1,2) \\)
\\( (-1,-2) \\)
\\( (2,1) \\)

Explanation:

Step1: Recall the standard form of hyperbola equation

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 \(k\)

In the given equation \(\frac{(x - 2)^2}{4^2}-\frac{(y - 1)^2}{2^2}=1\), by comparing with the standard form, we have \(h = 2\) and \(k=1\).

Answer:

\((2,1)\)