Questions: Graph the circle [ (x-1)^2+(y+2)^2=49 ]

Transcript text: Graph the circle \[ (x-1)^{2}+(y+2)^{2}=49 \]

Solution

Solution Steps

Step 1: Identify the Center and Radius of the Circle

The given equation of the circle is $(x-1)^{2}+(y+2)^{2}=49$. This is in the standard form $(x-h)^{2}+(y-k)^{2}=r^{2}$, where $(h, k)$ is the center and $r$ is the radius.

Step 2: Calculate the Center and Radius

From the equation, we can identify:

The center $(h, k)$ is $(1, -2)$.
The radius $r$ is $\sqrt{49} = 7$.

Final Answer

The circle has a center at $(1, -2)$ and a radius of $7$.

{"axisType": 3, "coordSystem": {"xmin": -6, "xmax": 8, "ymin": -9, "ymax": 5}, "commands": ["(x-1)2 + (y+2)2 = 49"], "latex_expressions": ["$(x-1)^{2}+(y+2)^{2}=49$"]}

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