Question

(a).Find the center and radius,then

(b).Graph the circle$x^2+y^2-2x-3=0$

Short answer

(a).Center $c=(1,0)$and radius $r=2$

(b).Graph of the circle.

Step-by-step solution

Part(a).Step 1.Given information

The equation of the given circle $x^2+y^2-2x-3=0$

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,

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

Which is the standard circle form with

circle=$(1,0)$

radius =$2$

Part b.Step 1.Given information

The equation of the given circle$x^2+y^2-2x-3=0$

Part b.Step 2.Graph of the circle.