Finding Radius Of Circle From Circle's Equation

Question

For basic equations like:-

$$ x^2 + y^2 = 4 $$

we can find out that the radius of the circle is 2. But for an equation like:-

$$ x^2 + (y+1)^2 = 1 $$

What will be the radius of the circle?

Answer 1

$x^2+(y+1)^2=1$ is a circle whose center is $(0,-1)$ and radius $1$. In general, $(x-a)^2+(y-b)^2=r^2$ is a circle whose center is $(a,b)$ and radius $|r|$.

Answer 2

The general equation for a circle in the plane centered at $(a,b)$ with radius $r$ is given by $$(x-a)^2+(y-b)^2 = r^2$$

The effect of $(x-a)$ is a horizontal shift of $a$-units while the effect of $(y-b)$ is a vertical shift of $b$-units.