Write the equation in standard form for the circle x^2+y^2–6y–9= 0.

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Identify equation and need: Identify the given equation and the need to complete the square for y. The given equation is x^2 + y^2 – 6y – 9 = 0. To get it into standard form, we need to complete the square for the y terms.Group and leave space: Group the y terms and leave a space to complete the square. x^2 + (y^2 – 6y + ___) - 9 = 0 + ___ We will determine the number to fill in the blanks that completes the square for the y terms.Calculate number to complete: Calculate the number needed to complete the square for y. To complete the square, we take half of the coefficient of y, which is -6, divide it by 2 to get -3, and then square it to get 9. This is the number we add to both sides of the equation.Add number to complete: Add the number to complete the square on both sides of the equation. x^2 + (y^2 – 6y + 9) - 9 = 0 + 9 Now the equation looks like this: x^2 + (y - 3)^2 - 9 + 9 = 0 + 9Simplify equation: Simplify the equation. x^2 + (y - 3)^2 = 9 This is the standard form of the circle's equation.

Write the equation in standard form for the circle $x^2+y^2-6y-9= 0$ .

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Write the equation in standard form for the circle x2+y2−6y−9=0x^2+y^2-6y-9= 0x2+y2−6y−9=0.

Write the equation in standard form for the circle $x^2+y^2-6y-9= 0$ .