☼ Equation of  a Circle :–

  Parametric Equation of  a circle with centre ( h, k) and radius = r  :

x  =  h + r cosθ and y  =  k + r sinθ  :  Where,  θ ∈ ( – π, π]

Parametric Equation of  a circle ( with centre origin ) :

x  =   r cosθ and y  =   r sinθ  :  Where,  θ ∈ ( – π, π] 

  Parametric Equation of  a circle ( with centre origin and radius = 1 ) :

x  =   cosθ and y  =   sinθ  :  Where,  θ ∈ ( – π, π] 

  Equation of  a circle with centre ( h, k) and radius = r  :

( x – h ) ² +  ( y – k ) ² =   r² 

  Equation of  a circle ( with centre origin ) :

x² +  y² =   r² 

  Equation of  a circle ( with centre origin and radius = 1 ) :

x² +  y² =   1

    The  equation of   a  circle with diametrically end–points  A (x₁, y₁)   and B (x₂, y₂)  is :

( x – x₁ )( x – x₂ ) + ( y – y₁ )( y – y₂ ) = 0 

  Equation of  a circle passing through two intersecting circles S₁ : x²  + y² + 2g₁x + 2f₁y + c₁ = 0  &  S₂ : x² + y² + 2g₂ x + 2f₂ y + c₂ = 0   is :

S₁ + λS₂  = 0

Click here to see next topic