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Determine the equation of the circle graphed below.

Determine the equation of the circle graphed below.-example-1

1 Answer

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Answer:


\displaystyle \large{(x-3)^2+(y+7)^2=9}

Explanation:

By looking at the graph, we can say that the circle has a center point at (3,-7). Next, find the radius which is the distance between center and an endpoint.

Distance Formula


\displaystyle \large{√((x_2-x_1)^2+(y_2-y_1)^2)}

Determine:

  • Center =
    \displaystyle \large{(x_2,y_2)} = (3,-7)
  • Endpoint =
    \displaystyle \large{(x_1,y_1)} = (0,-7)

Therefore:


\displaystyle \large{√((3-0)^2+(-7-(-7))^2)}\\\\\displaystyle \large{√(3^2+(-7+7)^2)}\\\\\displaystyle \large{√(9) = 3}

Therefore, radius = 3.

Equation of Circle


\displaystyle \large{(x-h)^2+(y-k)^2=r^2}

where:

  • (h,k) = center = (3,-7)
  • r = 3 so r² = 9

Hence:


\displaystyle \large{(x-3)^2+(y-(-7))^2=3^2}\\\\\displaystyle \large{(x-3)^2+(y+7)^2=9}

User Parth Raval
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