Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the relations domain and range.

$$ ( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 49 $$

what is the center of the circle?

the circle is centered at the point

(type an ordered pair.)

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^{2}+(y - k)^{2}=r^{2}\), where \((h,k)\) is the center of the circle.

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

For the equation \((x - 1)^{2}+(y - 2)^{2}=49\), comparing with \((x - h)^{2}+(y - k)^{2}=r^{2}\), we have \(h = 1\) and \(k=2\).

Answer:

\((1,2)\)