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x2+y2+6x−4y=3x^{2}+y^{2}+6x-4y=3\newlineA circle in the xyxy-plane has the equation shown. What is the yy-coordinate of the center of the circle?

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Find trigonometric ratios using the unit circleright chevron icon

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Q. x2+y2+6x−4y=3x^{2}+y^{2}+6x-4y=3\newlineA circle in the xyxy-plane has the equation shown. What is the yy-coordinate of the center of the circle?
  1. Rewrite Equation: Rewrite the given equation in the standard form of a circle by completing the square for both xx and yy terms.
  2. Complete x-square: Complete the square for the x-terms: x2+6xx^2 + 6x can be rewritten as (x+3)2−9(x+3)^2 - 9.
  3. Complete yy-square: Complete the square for the yy-terms: y2−4yy^2 - 4y can be rewritten as (y−2)2−4(y-2)^2 - 4.
  4. Simplify Equation: Simplify the equation by combining constants and moving them to the right side of the equation.
  5. Identify Center: Identify the center of the circle from the equation (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2, where (h,k)(h, k) is the center. Here, h=−3h = -3 and k=2k = 2.

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