Positional Relationship between a Line and a Circle (Discriminant Method)
The positional relationship between the line Ax + By + C = 0 and the circle (x - h)² + (y - k)² = r² can be determined by the discriminant Δ of the quadratic e…
Syllabus path: Geometry and Algebra › Plane Analytic Geometry › Equations and Properties of Circles
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CSCA Mathematics Formula Reference
Formula and explanation
The positional relationship between the line Ax + By + C = 0 and the circle (x - h)² + (y - k)² = r² can be determined by the discriminant Δ of the quadratic equation obtained by solving the system: - Δ > 0: Intersect (two intersection points). - Δ = 0: Tangent (one intersection point). - Δ < 0: Separate (no intersection points).
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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