Different Forms of Equation of a Circle

Different Forms of Equation of a Circle

This section develops three equivalent ways to write the equation of a circle, depending on what information a problem gives you:

1. Standard form — centre at the origin: $x^2+y^2=r^2$.
2. Centre-radius form — centre at any point $(h,k)$: $(x-h)^2+(y-k)^2=r^2$.
3. Diameter form — built from two diametrically opposite points $A(x_1,y_1)$, $B(x_2,y_2)$: $(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$. …