Toppers Notes on The Circles

Below you will get an embedded PDF file of the topic “toppers notes on The Circles for jee main & Advanced”, where you have the facility to read, download, or print the document at your convenience. You can take the help of these short notes for the preparation of all India engineering examinations like JEE Main & JEE Advanced. In fact, these notes are helpful to crack any entrance exam in which the mathematics up to 12th class is asked. 

Table of Content

  • Definition of a circle.
  • Standard equation of a circle.
  • General equation of a circle.
  • Condition for a general equation to represent a circle.
  • Different forms of the equation of a circle.
  • Diameter form of a circle.
  • Intercepts made by a circle on the co-ordinate axes.
  • Parametric equation of a circle.
  • Position of a point with respect to a circle.
  • Equation of circle through three non-collinear points.
  • The intersection of a straight line with the circle.
  • Length of an intercept made by a circle on a straight line.
  • Tangent to a circle at a given point.
  • Equation of tangent in slope form.
  • Condition of tangency.
  • Equation of normal to the circle.
  • Length of the tangent to a circle.
  • Equation of pair of tangents.
  • Director circle.
  • Power of a point with respect to a circle.
  • Chord of contact of tangents.
  • Common chord of two circles.
  • Pole and polar.
  • Conjugate points.
  • Conjugate lines.
  • The number of tangents to a circle.
  • Direct common tangents.
  • Transverse common tangents.
  • Image of a circle.
  • The angle of intersection of two circles.
  • Condition of orthogonality.
  • Family of circles.
  • Radical axis.
  • Properties of the radical axis.
  • The radical center.
  • Properties of the radical center.
  • Co-axial System of circles.
  • Limiting points.