Question

give the center and radius of the circle described by the equation and range.

what is the center of the circle?
the circle is centered at the point (0,0)
(type an ordered pair.)
what is the radius of the circle?
the radius of the circle is 7
(type an integer or a fraction.)
use the graphing tool to graph the circle
click to
enlarge
graph

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 and \(r\) is the radius.
For the equation \(x^{2}+y^{2}=49\) (rewriting \(x^{2}+y^{2}=49\) in the standard form \((x - 0)^2+(y - 0)^2=r^2\)).

Step2: Identify the center

Comparing \(x^{2}+y^{2}=49\) with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 0\) and \(k = 0\). So the center \((h,k)=(0,0)\).

Step3: Identify the radius

Since \(x^{2}+y^{2}=49=(x - 0)^2+(y - 0)^2=r^2\), then \(r^{2}=49\). Taking the square root of both sides (\(r>0\) as it represents a radius), we get \(r=\sqrt{49}=7\).

Answer:

The center of the circle is \((0,0)\) and the radius of the circle is \(7\).