Question

Identify the center and the radius of the circle.(x - 1)^2+ (y + 3) = 4

Answer 1

We are given the following equation of a circle.

`\mleft(x-1\mright)^2+(y+3)^2=4`

The standard form of the equation of a circle is given by

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

Comparing the given equation with the standard form we see that

`\begin{gathered} h=1 \\ k=-3 \\ r^2=4 \\ r=\sqrt[]{4} \\ r=2 \end{gathered}`

Therefore, the center of the circle is

`C=(h,k)=(1,-3)`

Therefore, the radius of the circle is

`r=2`