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Given equation of a circle: x^2 – 4x + y^2 + 6y = 12 rewrite it in a standard form. Find its radius and coordinates of its center. Standard Form:_____

r:_____

Center:____

Given equation of a circle x2 4x y2 6y 12 rewrite it in a standard form Find its radius and coordinates of its center Standard Form r Center class=

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Answer:

The standard form is:

  • (x - h)² + (y - k)² = r², where (h, k) is the center, r is the radius

Convert the given into standard form by completing square:

  • x² - 4x + y² + 6y = 12
  • x² - 4x + 4 + y² + 6y + 9 = 12 + 4 + 9
  • (x - 2)² + (y + 3)² = 25
  • (x - 2)² + (y + 3)² = 5²
  • The standard form is above.
  • The center is (h, k) = (2, -3)
  • The radius is r = 5

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