Question

(a) Find the center and radius, then (b) graph the circle:$x^2+y^2+6x-2y+1=0$

Short answer

The center and the radius of the circle are $(-3,1)$ and $r=3$respectively. The graph of this circle is:

Step-by-step solution

Part (a) Step 1. Given information.

The equation of the circle is$x^2+y^2+6x-2y+1=0$

We have to find radius and center.

Also, we have to graph this circle.

Part (a) Step 2. Complete the squares

Collect the x- and y- terms,

$$\begin{gathered} x^2+y^2+6x-2y+1=0 \\ {x}^2+6x+y^2-2y=-1 \\ {x}^2+6x+9+y^2-2y+1=-1+9+1 \\ {(x+3)}^2+{(y-1)}^2=3^2 \end{gathered}$$

Part (a) Step 3. Compare with the standard form of a circle to find radius and center 

Compare ${(x+3)}^2+{(y-1)}^2=3^2$with the standard form ${(x-h)}^2+{(y-k)}^2=r^2$

We have, role="math" localid="1645269841711" $(h,k)=(-3,1)$(centre)

$r=3$(radius)

Part (b) Step 1. Graph the circle

The graph is: