Equation of the Tangent Line to a Circle (Given Point of Tangency)
Given a point P(x₀, y₀) on the circle (x - h)² + (y - k)² = r², the equation of the tangent line at P is: (x₀ - h)(x - h) + (y₀ - k)(y - k) = r². This is a con…
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.
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CSCA Mathematics Formula Reference
Formula and explanation
Given a point P(x₀, y₀) on the circle (x - h)² + (y - k)² = r², the equation of the tangent line at P is: (x₀ - h)(x - h) + (y₀ - k)(y - k) = r². This is a convenient formula for finding the tangent line when the point of tangency is known.
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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