Toppers Notes on The Ellipse

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Table of Content

  • Definition of the ellipse.
  • Standard equation of the ellipse.
  • The parametric form of the ellipse.
  • Position of a point with respect to the ellipse.
  • The intersection of a line and an ellipse.
  • Equation of tangents in different forms.
  • Equation of normal in different forms.
  • Auxillary circle.
  • The eccentric angle of a point.
  • The equation of pair of tangents.
  • The director circle.
  • The chord of contact.
  • The equation of the chord which bisected at a given point.
  • The equation of a chord joining two points on the ellipse.
  • Pole and polar.
  • The equation of polar.
  • Properties of pole and polar.
  • The diameter of the ellipse.
  • Conjugate diameters of the ellipse.
  • The properties of the diameters.
  • The properties of the conjugate diameters.
  • Equi-conjugate diameters.
  • Subtangent and subnormal.
  • Properties of the ellipse.