Question

In the following exercises, (a) find the centre and radius, then (b) graph each circle.

${(x+2)}^2+{(y-5)}^2=4$

Short answer

The centre of circle is $(-2,5)$ and radius is $2$.

Step-by-step solution

Step 1. Given information

The given equation of circle is${(x+2)}^2+{(y-5)}^2=4$

Step 2. Part (a) Find the centre and radius of circle.

${(x+2)}^2+{(y-5)}^2=2^2$

On comparing with the standard form of equation ${(x-h)}^2+{(y-k)}^2=r^2$,

$$\begin{gathered} h=-2 \\ k=5 \\ r=2 \end{gathered}$$

Therefore, the centre of circle is $(-2,5)$ and radius is $2$.

Step 3. Part (b) The graph of circle.