Chapter 9.2, Problem 43WE

To determine

To graph: Plot the graph for the given equation.

Explanation of Solution

Given information: It is given that $y=\sqrt{25-x^2}$ and $\sqrt{a}\ge 0$

Calculation: As we know that a circle ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ with center $\left(h,k\right)$ and radius $\left(r\right)$ .

Now, the top half of the circle i.e. semicircle:

  $\begin{array}{l}y=\sqrt{25-x^2}\\ y^2=25-x^2\\ x^2+y^2=25\\ x^2+y^2=5^2\end{array}$

Compare ${\left(x-0\right)}^2+{\left(y-0\right)}^2=5^2$ to ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , we get,

• The center $\left(h,k\right)=\left(0,0\right)$
• The radius $r=5$

Graph: The required one $\left(y=\sqrt{25-x^2}\right)$ is plotted below,