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Find the center and the radius of the circle. Then graph the circle. (x+3)^(2)+(y-1)^(2)=16 Use the graphing tool to graph the circle.

Find the center and the radius of the circle. Then graph the circle.\newline(x+3)2+(y−1)2=16 (x+3)^{2}+(y-1)^{2}=16 \newlineUse the graphing tool to graph the circle.

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Full solution

Q. Find the center and the radius of the circle. Then graph the circle.\newline(x+3)2+(y−1)2=16 (x+3)^{2}+(y-1)^{2}=16 \newlineUse the graphing tool to graph the circle.
  1. Identify Equation Form: Identify the standard form of the circle's equation and compare it to the given equation.\newlineStandard form: (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2\newlineGiven equation: (x+3)2+(y−1)2=16(x + 3)^2 + (y - 1)^2 = 16\newlineHere, h=−3h = -3, k=1k = 1, and r2=16r^2 = 16.
  2. Calculate Radius: Calculate the radius of the circle by taking the square root of r2r^2.\newliner=16r = \sqrt{16}\newliner=4r = 4
  3. Summarize Center and Radius: Summarize the center and radius of the circle.\newlineCenter: (−3,1)(-3, 1)\newlineRadius: 44
  4. Graph Circle: Graph the circle using the center and radius.\newlinePlot the center at (−3,1)(-3, 1).\newlineDraw a circle with radius 44 around the center.

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