complete the square to rewrite the following equation in standard form. show all necessary work. x² - 2x y² 6y = 15



Answer :

To rewrite the equation in standard form by completing the square, follow these steps:

  • Move the constant term to the other side.
  • Complete the square for the x-terms.
  • Complete the square for the y-terms.
  • Rewrite the equation with the squared terms factored.
  • The equation in standard form after completing the square is: (x-1)² + (y-3)² = 25.
  • Move the constant term to the other side of the equation: x^2 - 2x + y^2 - 6y = 15
  • Complete the square for the x-terms by adding and subtracting (2 - 2)^2 = 1: x^2 - 2x + 1 + y^2 - 6y = 15 + 1
  • Complete the square for the y-terms by adding and subtracting (2 - 6)^2 = 9: x^2 - 2x + 1 + y^2 - 6y + 9 = 15 + 1 + 9
  • Rewrite the equation with the squared terms factored: (x - 1)^2 + (y - 3)^2 = 25

Therefore, the equation in standard form after completing the square is: (x - 1)^2 + (y - 3)^2 = 25