Question

(a).Find the center and radius,then

(b).Graph the circle$x^2+y^2-12y+11=0$

Short answer

(a). Center $c=(0,6)$and radius $r=5$

(b). Graph of the circle

Step-by-step solution

Part(a). Step 1.Given information

The equation of the given circle$x^2+y^2-12y+11=0$

We have to find radius and center.

Also, we have to graph this circle.

Part (a) Step 2. Converting into standard circle form

find the values of x and y- terms,

$$\begin{gathered} x^2+y^2-12y+11=0 \\ {x}^2+y^2-12y=-11 \\ {x}^2+y^2-12y+36=-11+36 \\ (x^2-0)+(y^2-12y+36)=25 \\ {(x-0)}^2+{(y-6)}^2=5^2 \end{gathered}$$

Which is the standard circle form with

circle=$(0,6)$

radius =$5$

Part b.Step 1.Given information

The equation of the given circle$x^2+y^2-12y+11=0$

Part b.Step 2.Graph of the circle.