Tangents, Normals and Coordinate Geometry Summary

Tangents and Normals

Summary

by differentiating and finding the derived or gradient function we obtain an equation which will give the gradient at any point on a curve.

the gradient for a particular value of x can then be obtained by substitution.

for the conic sections, the circle, the ellipse, the parabola and the hyperbola differentiation can be done implicitly on the cartesian (x, y) equation or by using the chain rule on the parametric equations.

 

once the gradient of a tangent to a curve has been found, the equation of the tangent or the normal (perpendicular to the tangent) can be found.

Key Skills

find the equation of the tangents and normals at points on functions and relations especially the conic sections:

  • the circle
  • the ellipse
  • the parabola
  • the hyperbola

Vocabulary

parametric equation, implicit functionconic sections,hyperbolaellipse, parabolatangentnormaldifferentiation.