Question

Find the center and radius of the circle $x^2+4x+y^2-2y-4=0.$Graph the circle.

Short answer

The radius and center of circle is 3units and$(-2,1)$ respectively

The graph can be given as

Step-by-step solution

Given information

The equation of the circle is$x^2+4x+y^2-2y-4=0.$

Arrange the equation

We get

$$\begin{gathered} x^2+4x+y^2-2y-4=0. \\ {x}^2+4x+4+y^2-2y+1-4-1=4 \\ {(x+2)}^2+{(y-1)}^2=9(x+2{)}^2+{(y-1)}^2=3^2 \end{gathered}$$

Find the radius and center

On comparing with standard equation we get$radius=3$and center$=(-2,1)$

Plot the graph

The graph can be given as

Conclusion

The radius of the circle is 3 units and center is$(-2,1)$

The graph of the circle is