Diameter Form Equation of a Circle
Formula: (x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0 Conditions: Points A(x₁, y₁) and B(x₂, y₂) are the endpoints of a diameter of the circle. Explanation: This eq…
Syllabus path: Geometry and Algebra › Plane Analytic Geometry › Equations and Properties of Circles
CSCA Exam Prep
This formula is aligned to the CSCA undergraduate admissions exam syllabus. Continue with the linked tutorial and topic practice.
Practice related questions (11) · Start mock exam · Sign up — AI explanations · Membership plans
CSCA Mathematics Formula Reference
Formula and explanation
Formula: (x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0 Conditions: Points A(x₁, y₁) and B(x₂, y₂) are the endpoints of a diameter of the circle. Explanation: This equation represents the circle with A and B as endpoints of a diameter. Its geometric basis is the Inscribed Angle Theorem: the angle subtended by a diameter is a right angle, i.e., PA · PB = 0.
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…
Plan your next CSCA study step
Use this topic in a focused practice set, then connect it to the exam requirements and timed papers.