x^(2)+y^(2)+6x-4y=3 A circle in the xy-plane has the equation shown. What is the y coordinate of the center of the circle?

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x^(2)+y^(2)+6x-4y=3 A circle in the  xy-plane has the equation shown. What is the  y coordinate of the center of the circle?

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Rewriting the equation: To find the center of the circle, we need to rewrite the equation in the standard form of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle. We will complete the square for both x and y.Grouping the terms: First, we group the x terms and the y terms together: (x^2 + 6x) + (y^2 - 4y) = 3.Completing the square for x terms: To complete the square for the x terms, we take half of the coefficient of x, which is 6/2 = 3, and square it, adding 3^2 = 9 to both sides of the equation.Completing the square for y terms: Similarly, to complete the square for the y terms, we take half of the coefficient of y, which is -4/2 = -2, and square it, adding (-2)^2 = 4 to both sides of the equation.Adding constants to both sides: Now we add 9 and 4 to both sides of the equation to maintain equality: (x^2 + 6x + 9) + (y^2 - 4y + 4) = 3 + 9 + 4.Simplifying the right side: Simplify the right side of the equation: 3 + 9 + 4 = 16.Standard form of the equation: The equation now looks like this: (x^2 + 6x + 9) + (y^2 - 4y + 4) = 16.Finding the center of the circle: We can now rewrite the equation as (x + 3)^2 + (y - 2)^2 = 16, which is in the standard form of a circle.The y-coordinate of the center: From the standard form (x + 3)^2 + (y - 2)^2 = 16, we can see that the center of the circle is at (-3, 2).The y-coordinate of the center of the circle is 2.

$x^{2}+y^{2}+6 x-4 y=3$ $\newline$ A circle in the $x y$ -plane has the equation shown. What is the $y$ coordinate of the center of the circle?

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

$x^{2}+y^{2}+6 x-4 y=3$ $\newline$ A circle in the $x y$ -plane has the equation shown. What is the $y$ coordinate of the center of the circle?