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1. Equation of a circle in the centre radius form

(x - h)^{2} + (y - k)^{2} = a^{2} where, radius is 'a' and centre is c(h, k).

2. Equation of a circle in the diameter form

(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0 where, A(x_{1}, y_{1}) and B(x_{2}, y_{2}) are the extremities of the diameter.

3. General equation of a circle

x^{2} + y^{2} + 2gx + 2fy + c = 0 where, centre is (- g, - f) and radius =

4. Parametric equations of a circle

x = a cosq, y = a sinq are the parametric equations of the circle x^{2} + y^{2} = a^{2}.

5. Circles touching internally and externally

If x^{2} + y^{2} + 2g_{1} x + 2f_{1} y + c_{1} = 0 and x^{2} + y^{2} + 2g_{2}x + 2f_{2} y + c_{2} = 0 are the equations of the two circles touching one another, then their centres are given by C_{1} º (- g_{1}, - f_{1}), C_{2 }º (- g_{2}, - f_{2}) and their radii are r_{1} = , r_{2} =

6. Equation of the tangent to a circle with origin as centre

The equation of the tangent to the circle x^{2} + y^{2} = a^{2} at a point P(x_{1}, y_{1}) on it is given as xx_{1} + yy_{1} = a^{2}, where P(x_{1}, y_{1}) is a point in the circle and the tangent and 'a' is the radius.

7. Equation of the tangent to a circle at a point (x_{1}, y_{1})

The equation of the tangent to the circle x^{2} + y^{2} + 2gx + 2fy + c = 0 at a point P (x_{1}, y_{1}) on it is xx_{1} + yy_{1} + g(x + x_{1}) + f(y + y_{1}) + c = 0