tangents and normals
What tangents and normals means in Mathematics A-Level, as defined for AQA, WJEC.
Definitions of tangents and normals
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Reference: AQA
The tangent at a point has equation y - y1 = m(x - x1), where m is the gradient, and the normal is perpendicular, so its gradient is -1/m provided m ≠ 0.
The tangent at a point has gradient m = f'(x₁) and equation y − y₁ = m(x − x₁); the normal is perpendicular with gradient −1/m.
Analysed using the perpendicularity of the radius to the tangent at the point of contact.
Topics that use tangents and normals
- G: Differentiation (AQA A-Level)
- Coordinate geometry in the (x, y) plane (AS Unit 1: Pure Mathematics A) (WJEC A-Level)
- Differentiation (AS Unit 1: Pure Mathematics A) (WJEC A-Level)
Related terms
- Derivative
- Normal
- rate of change
- Stationary point
- Tangent
- algebraic preparation
- angle in a semicircle
- Chain rule
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