The document discusses the general form of a circle equation: x2 + y2 + Cx + Dy + E = 0. It provides examples of converting between general form and center-radius form, finding the radius and center of circles in general form, and writing the equation of a circle given its center and radius. Practice problems apply these skills, such as finding the area and circumference of circles defined by general form equations.

1. Day 3 ­ General Form of a Circle
General Form of a Circle
x2 + y2 + Cx + Dy + E = 0 C, D, E are constants
Ex. 1: Find the center and radius of the circle x2 + y2 + 8x + 6y = 0.
Sketch the circle.
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2. Practice 1: Convert the equation x2 + y2 + 26x + 10y + 12 = 0 into center­
radius form. Find the radius and center.
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3. Example 2: Write the equation of a circle in general form that has a
center (4, ­3) and radius of 7.
Practice 2: Write the equation of a circle in general form that has a
center (0, 5) and radius of √13.
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4. Example 3: Find the area of the circle
2x2 + 2y2 + 20x ­ 12y + 19 = 0
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5. Practice 3: Find the circumference of the circle
4x2 + 4y2 ­ 56x + 48y + 75 = 0
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