Chapter 9, Problem 4T

To determine

Calculation:

To find the radius of the circle, we find the distance between the two points $\left(0,4\right)\text{ and }\left(-2,5\right)$ , we substitute $\left(x_1,y_1\right)=\left(0,4\right)$ and $\left(x_2,y_2\right)=\left(-2,5\right)$ in the above distance formula. So we get $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(-2-0\right)}^2+{\left(5-4\right)}^2}\text{Substitute }\left(x_1,y_1\right)=\left(0,4\right),\left(x_2,y_2\right)=\left(-2,5\right)\\ =\sqrt{{\left(-2\right)}^2+{\left(1\right)}^2}\text{Simplify}\\ =\sqrt{4+1}\\ =\sqrt{5}\end{array}$ Thus the Thus the radius of the circle is $\sqrt{5}\text{ units}$.

(b)

To Write: The equation of the circle in standard form.