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(x+3)^(2)+(y-4)^(2)=9 A circle in the xy-plane has the equation shown. If the x-coordinate of a point on the circle is -3 , what is a possible corresponding y-coordinate?

(x+3)2+(y−4)2=9 (x+3)^{2}+(y-4)^{2}=9 \newlineA circle in the xy x y -plane has the equation shown. If the x x -coordinate of a point on the circle is −3-3 , what is a possible corresponding y y -coordinate?

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Q. (x+3)2+(y−4)2=9 (x+3)^{2}+(y-4)^{2}=9 \newlineA circle in the xy x y -plane has the equation shown. If the x x -coordinate of a point on the circle is −3-3 , what is a possible corresponding y y -coordinate?
  1. Plug x=−3x = -3: Plug x=−3x = -3 into the equation to find the corresponding y-coordinate.\newline(−3+3)2+(y−4)2=9(-3+3)^2 + (y-4)^2 = 9
  2. Simplify left side: Simplify the left side of the equation.\newline(0)2+(y−4)2=9(0)^2 + (y-4)^2 = 9
  3. Solve for (y−4)(y-4): Solve for (y−4)2(y-4)^2.(y−4)2=9(y-4)^2 = 9
  4. Take square root: Take the square root of both sides to solve for y−4y-4.\newliney−4=±3y-4 = \pm 3
  5. Add 44 to solve: Add 44 to both sides to solve for yy.\newliney=4±3y = 4 \pm 3
  6. Find possible values: Find the two possible values for yy.y=4+3y = 4 + 3 or y=4−3y = 4 - 3y=7y = 7 or y=1y = 1

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