What is a circle?
A circle is a locus of a point which moves in a plane, such that its distance from a fixed point in the plane is always constant.
The fixed point is called the centre of the circle and the constant is called its radius.
The equation of the circle: Its the set of all points lying on the circumference of the circle.
Chord and diameter of the circle: The line joining any two points on the circumference is called a chord. If any chord passing through its centre is called its diameter.
diameter d= 2r
Equation of the circle in different forms
(a). Centre- radius form :
This equation is known as central form of the equation of a circle.
NOTE: when centre (0, 0) then the equation of the circle becomes
which is known as the standard form of the circle.
(b) Parametric form : The parametric equation of the circle are
(c) General form: The equation of the circle with centre ( h, k) and radius r is
Which is of the form +2gx+2fy+c=0.
Relative positions of two circles:
Pole, polar , chord of contact, conjugate lines and conjugate points