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

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Convert equations of circles from general to standard formright chevron icon

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Q. Write the equation in standard form for the circle x2+y2−6y−9=0x^2+y^2-6y-9= 0.
  1. Identify equation and need: Identify the given equation and the need to complete the square for yy.\newlineThe given equation is x2+y2−6y−9=0x^2 + y^2 - 6y - 9 = 0. To get it into standard form, we need to complete the square for the yy terms.
  2. Group and leave space: Group the yy terms and leave a space to complete the square.x2+(y2−6y+__)−9=0+__x^2 + (y^2 - 6y + \_\_) - 9 = 0 + \_\_We will determine the number to fill in the blanks that completes the square for the yy terms.
  3. Calculate number to complete: Calculate the number needed to complete the square for yy.\newlineTo complete the square, we take half of the coefficient of yy, which is −6-6, divide it by 22 to get −3-3, and then square it to get 99. This is the number we add to both sides of the equation.
  4. Add number to complete: Add the number to complete the square on both sides of the equation.\newlinex2+(y2−6y+9)−9=0+9x^2 + (y^2 - 6y + 9) - 9 = 0 + 9\newlineNow the equation looks like this:\newlinex2+(y−3)2−9+9=0+9x^2 + (y - 3)^2 - 9 + 9 = 0 + 9
  5. Simplify equation: Simplify the equation. x2+(y−3)2=9x^2 + (y - 3)^2 = 9 This is the standard form of the circle's equation.

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