General Equation of a Circle
Formula: x² + y² + Dx + Ey + F = 0 Conditions: It represents a circle when D² + E² - 4F > 0. Explanation: This is the expanded form of the circle's equation. T…
Syllabus path: Geometry and Algebra › Plane Analytic Geometry › Equations and Properties of Circles
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CSCA Mathematics Formula Reference
Formula and explanation
Formula: x² + y² + Dx + Ey + F = 0 Conditions: It represents a circle when D² + E² - 4F > 0. Explanation: This is the expanded form of the circle's equation. The center is at ( - (D)/(2), - (E)/(2)) and the radius is r = (1)/(2)√(D² + E² - 4F). When D² + E² - 4F = 0, it represents a single point (point circle); when less than 0, it represents no real graph.
Related tutorial and examples
Equations and Properties of Circles
Equations and Properties of Circles Circles are a core topic in the CSCA geometry section, often tested in combination with lines and distance formulas. Mastering the two forms of circle equations and the "distance from center to line" is key to solving these problems. 1. Definit…
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