Circles

Circle is a probably the easiest of all the conic sections, and also helps in other conic sections.

Past year trend

As we can see from the graph, there is not even a single year when questions are not asked from circles both in JEE-Advanced and JEE-Mains.

Topics

Circles is one of the basic conic which is a special case of ellipse. The general equation of a circle with radius r and centre as !!(a,b)!! is given by !!(x-a)^2+(y-b)^2=r^2!!.

For a circle !!(x)^2+(y)^2=a^2!!:

The equation of tangent is given by !!xcostheta+ysintheta=a!!.

The chord of contact from a point (p,q) is !!px+qy=a^2!!.

The equation of a director circle is !!x^2+y^2=2a^2!!.

For two circles !!S_1!! and !!S_2!!, family of circles is given by !!S_1+lambdaS_2=0!! and radical axis is given by !!S_1-S_2=0!!.

Questions are asked related to:

  1. Equation of a circle given a set of conditions
  2. Point of intersection of circle and another conic
  3. Locus of point of contact/ intersection of tangents and chords