Circle 2

• General form of the equation of a circle

  x^2 + y^2 + dx + ey + f = 0
• Deriving general form from standard form

  1. Expand (x - h)^2 + (y - k)^2 = r^2

  2. Combine and simplify terms

  3. Let d = -2h, e = -2k, f = h^2 + k^2 - r^2
• Deriving standard form from general form

  1. Rearrange terms to get perfect square trinomials

  2. Complete the square for x and y terms

  3. Simplify
• Center of a circle


  The point (h, k) where h is the x-coordinate and k is the y-coordinate
• Radius of a circle

  The distance from the center to the circumference, denoted by r
• The general form of the equation of a circle is x^2 + y^2 + dx + ey + f = 0
• To find the center and radius from the general form, we need to rearrange the terms to get perfect square trinomials
• Completing the square is a key technique for deriving the standard form from the general form
• General form of the equation of a circle

  x^2 + y^2 + dx + ey + f = 0
• Deriving general form from standard form

  1. Expand (x - h)^2 + (y - k)^2 = r^2

  2. Combine and simplify terms

  3. Let d = -2h, e = -2k, f = h^2 + k^2 - r^2
• Deriving standard form from general form

  1. Rearrange terms to get perfect square trinomials

  2. Complete the square for x and y terms

  3. Simplify
• Center of a circle

  The point (h, k) where h is the x-coordinate and k is the y-coordinate
• Radius of a circle

  The distance from the center to the circumference, denoted by r
• The general form of the equation of a circle is x^2 + y^2 + dx + ey + f = 0
• To find the center and radius from the general form, rearrange to get perfect square trinomials, complete the square, and take the square root of the constant term