Chapter 9.2, Problem 9WE

To determine

To graph: Plot the graph for the given equation.

Explanation of Solution

Given information: It is given that $x^2+y^2=25$ .

Calculation: Simplify the given equation in terms of a general form.

  $\begin{array}{l}{x}^2+y^2=25\\ \therefore y^2=25-x^2\\ \therefore y=\sqrt{25-x^2}\end{array}$

Now, get the different value of y by putting x,

  $\begin{array}{ccc}x& 0& 5\\ y=\sqrt{25-x^2}& 5& 0\end{array}$

Graph: The required graph is given below.

  

Interpretation: A circle’s points are equidistant from a fixed point (center).

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

Hence,

  $\left(h,k\right)=\left(0,0\right)$ and $r=\sqrt{25}=5$

Now, substitute this value in the equation ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , we get,

  $\begin{array}{l}{\left(x-0\right)}^2+{\left(y-0\right)}^2=5^2\\ x^2+y^2=25\end{array}$