Question

find the center and the radius of the circle. then graph the circle.
( x^2 + y^2 = 10 )

the center is (0,0).
(type an ordered pair. type an integer or a fraction.)
the radius is 4.
(type an integer or a fraction.)
use the graphing tool on the right to graph the circle.
click to enlarge graph

Explanation:

Step1: Recall the standard circle 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.

Step2: Compare with given equation

The given equation is \(x^2 + y^2 = 10\). We can rewrite it as \((x - 0)^2 + (y - 0)^2 = (\sqrt{10})^2\).

Step3: Identify center and radius

By comparing with the standard form, we see that \(h = 0\), \(k = 0\), so the center is \((0, 0)\). And \(r^2 = 10\), so \(r=\sqrt{10}\) (since radius is positive).

Answer:

The center is \((0, 0)\). The radius is \(\sqrt{10}\).