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Analytic Geometry2D

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

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

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Interactive Tangent & Normal Explorer

Curve Factor c0.50
Point of Tangency x₀1.50
Point P:(1.50, -0.88)
Tangent Slope (m_t):1.500
Normal Slope (m_n):-0.667
Slope Product:-1.00
Click or drag on canvas to position P
Tangent Liney=1.50x+(−3.13)y = 1.50x + (-3.13)
Normal Liney=−0.67x+(0.13)y = -0.67x + (0.13)
Slope Perpendicularity Identity: mtangent⋅mnormal=−1m_{tangent} \cdot m_{normal} = -1

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