Standard form of equation of a circle

The equation of a circle in standard form is written as follows:

`(x - h)^2 + (y - k)^2 = r^2`

- where 'h' and 'k' are the x and y coordinates of the center of the circle respectively and 'r' is the length of the radius of the circle.

If you expand the formula, it becomes

`x^2 + y^2 - 2hx - 2ky + h^2 + k^2 = r^2`

In the above equation, we can see that both x and y have the same coefficient, 1. Thus, we can conclude that the coefficients of x and y are both same in the equation of a circle.

Further, if a circle has its center at the origin (thereby having center (0, 0)) and radius 1, then its equation in the standard form is

`x^2 + y^2 = 1`

This equation graphed on a coordinate plane looks like the following figure:

Circle having center at origin and radius 1