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Analytic Geometry2D

Tangents and Normals to Conic Sections - Theory & Concepts - Analytic Geometry Tangent Normal

Equations of tangent and normal lines to circles, parabolas, ellipses, and hyperbolas.

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Tangent and Normal to a Circle

Visualize the orthogonal relationship between tangent and normal vectors on a circle

45°
Mathematical Equations
Circle Equation:
x2+y2=1002x^2 + y^2 = 100^2
Tangent Equation:
x⋅(71)+y⋅(71)=1002x \cdot (71) + y \cdot (71) = 100^2
Normal Equation:
(71)y−(71)x=0(71) y - (71) x = 0
Observation: The normal line always passes directly through the origin (center of the circle), and the tangent line is always strictly perpendicular ($90^\circ$) to the normal line at the point of contact.

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