Chapter 9.2, Problem 27WE

To determine

To graph: Plot the graph for the given equality.

Explanation of Solution

Given information: It is given that $x^2+y^2-4y>0$ .

Calculation: Let a circle has the center $\left(h,k\right)$ and radius of $r$ then the equation of the circle is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ .

Rewrite $x^2+y^2<4$ in the form of standard circle equation,

  ${\left(x-0\right)}^2+{\left(y-0\right)}^2=2^2$

Hence,

  $\left(h,k\right)=\left(0,0\right)$ and $r=\sqrt{4}=2$

Graph: The required graph is given below.

  

Interpretation: The circle’s points are equidistant from a fixed point $\left(0,0\right)$ . And its radius is 2.