Chapter 11, Problem 8CR

To determine

To graph: The function of $x^2+y^2-2y+4y-11=0$ .

Explanation of Solution

Given information:

The given function is $x^2+y^2-2y+4y-11=0$ .

Graph:

Consider the equation of the circle can be simplified to the form of the circle given above.

  $\begin{array}{c}{x}^2+y^2-2y+4y-11=0\\ \left(x^2-2x+1\right)+\left(y^2+4y+4\right)=11+1+4\\ {\left(x-1\right)}^2+{\left(y+2\right)}^2=4^2\end{array}$

Therefore, the coordinates of the center of the given are $\left(1,-2\right)$ and the radius of the circle is $a=4$ units.

The graph for the given functions $x^2+y^2-2y+4y-11=0$ is shown in figure (1).

  

Figure (1)

Interpretation: Graph for the functions $x^2+y^2-2y+4y-11=0$ shows in figure (1).