Problem

Find the center and the radius of the circle. Then graph the circle. \[ x^{2}+y^{2}=49 \] The center is (Simplify your answer. Type an ordered pair.)

Solution

Step 1 :The given equation is already in the standard form of a circle equation, which is \(x^{2}+y^{2}=r^{2}\).

Step 2 :The center of the circle is at the origin (0,0) because there are no \(x\) or \(y\) terms.

Step 3 :The radius of the circle is the square root of the constant term on the right side of the equation. So, \(r=\sqrt{49}=7\).

Step 4 :Therefore, the center of the circle is \(\boxed{(0, 0)}\) and the radius is \(\boxed{7}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8112/

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