Equation of a circle

When Centre lies on x-axis

$(1)\,\,\,\,\,$ ${(x-a)}^2 + y^2 = r^2$

$(2)\,\,\,\,\,$ $x^2 + y^2 -2ax + a^2 -r^2 = 0$

Learn proof of equation of a circle when centre lies on x-axis without touching $y$-axis.

When Centre lies on y-axis

$(1)\,\,\,\,\,$ $x^2 + {(y-b)}^2 = r^2$

$(1)\,\,\,\,\,$ $x^2 + y^2 -2by + b^2 -r^2 = 0$

Learn proof of equation of a circle when centre lies on y-axis without touching x-axis.