Questions: 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.)

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

Solution

Solution Steps

Step 1: Identify the Equation of the Circle

The given equation is: \[ x^{2} + y^{2} = 49 \]

Step 2: Determine the Center of the Circle

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. Comparing this with the given equation, we see that $h = 0$ and $k = 0$.

Step 3: Determine the Radius of the Circle

The right side of the equation is $49$, which is $r^{2}$. Therefore, the radius $r$ is: \[ r = \sqrt{49} = 7 \]

Final Answer

The center is $(0, 0)$ and the radius is $7$.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["x2 + y2 = 49"], "latex_expressions": ["$x^{2} + y^{2} = 49$"]}

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