Chapter 9.2, Problem 35WE

To determine

To find: The equation of the circle.

Answer to Problem 35WE

The required equation is $x^2+{\left(y-5\right)}^2=25$ .

Explanation of Solution

Given information: The given points are $Center\left(0,5\right)$ and $\left(0,0\right)$ .

Formula used: Distance formula $D=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$ and ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

Calculation: First of all, finding the length of the radius by using the distance formula.

Hence,

  $\begin{array}{l}r=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(0-0\right)}^2+{\left(5-0\right)}^2}\\ =\sqrt{25}\\ =5\end{array}$

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

  $\begin{array}{l}\therefore {\left(x-0\right)}^2+{\left(y-5\right)}^2=25\left\{\because \left(h,k\right)=\left(0,5\right);r=5\right\}\\ \therefore x^2+{\left(y-5\right)}^2=25\end{array}$

Therefore, the required equation is $x^2+{\left(y-5\right)}^2=25$ .

The graph is given below,