**Equation of a Circle :**

**( x – h )**^{2 }+ ( y – k )^{2} = r^{2 }

If **centre** is **origin** —

**Centre** : O ( 0 , 0 )

**Radius** : r

( x – 0 )^{2 }+ ( y – 0 )^{2} = r^{2 }

**x **^{2 }+ y^{2} = r^{2 }

**Equation of a circle in different situations :**

**Case 1 : Centre ( h , k ) and passes through the origin(0 , 0)**

r = √(h – 0) ^{2 }+ (k – 0)^{2} = h ^{2 }+ k^{2}

r = √(h ^{2 }+ k^{2} )

( x – h )^{2 }+ ( y – k )^{2} = h ^{2 }+ k^{2}

**x **^{2 }+ y^{2 }— 2.h.x — 2.k.y = 0

**Case 2 : Centre ( h , k ) and touches the x-axis.**