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Google Classroom (x+4)^(2)+(y-1)^(2)=9 Which of the following is a graph of the given equation? Choose 1 answer: (A) Do 4 problems

Google Classroom\newline(x+4)2+(y−1)2=9 (x+4)^{2}+(y-1)^{2}=9 \newlineWhich of the following is a graph of the given equation?\newlineChoose 11 answer:\newline(A)\newlineDo 44 problems

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Full solution

Q. Google Classroom\newline(x+4)2+(y−1)2=9 (x+4)^{2}+(y-1)^{2}=9 \newlineWhich of the following is a graph of the given equation?\newlineChoose 11 answer:\newline(A)\newlineDo 44 problems
  1. Recognize Equation Form: Recognize the form of the equation.\newlineThe equation (x+4)2+(y−1)2=9(x+4)^{2}+(y-1)^{2}=9 is in the form of a circle's equation, which is (x−h)2+(y−k)2=r2(x-h)^{2}+(y-k)^{2}=r^{2}, where (h,k)(h,k) is the center of the circle and rr is the radius.
  2. Identify Center and Radius: Identify the center and radius of the circle.\newlineFrom the given equation, we can see that h=−4h=-4 and k=1k=1, which gives us the center of the circle at (−4,1)(-4,1). The radius rr is the square root of 99, which is 33.
  3. Determine Graph: Determine the graph based on the center and radius.\newlineThe graph of the equation is a circle with center at (−4,1)(-4,1) and radius 33. This means the circle is centered at the point (−4,1)(-4,1) and extends 33 units in all directions from that point.

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