Chapter 13.7, Problem 13PSB

(a)

To determine

To find:The equation of circle.

Answer to Problem 13PSB

The equation of circle is ${\left(x+3\right)}^2+{\left(y-3\right)}^2=3^2$ .

Explanation of Solution

The general equation of circle is given by,

  ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

The centre of circle is $\left(h,k\right)=\left(-3,3\right)$ and the radius of the circle is $r=3\text{unit}$ .

Substitute the values in the above expression.

  $\begin{array}{c}{\left(x-\left(-3\right)\right)}^2+{\left(y-3\right)}^2=3^2\\ {\left(x+3\right)}^2+{\left(y-3\right)}^2=3^2\end{array}$

Therefore, the equation of circle is ${\left(x+3\right)}^2+{\left(y-3\right)}^2=3^2$ .

(b)

To determine

To find: The area of shaded region.

Answer to Problem 13PSB

The area of shaded region isis $2\text{sq}\text{.units}$ .

Explanation of Solution

The area of shaded region is calculated as,

  $\begin{array}{c}A=3\times 3-\frac{\pi }{4}{3}^2\\ \approx 2\text{sq}\text{.unit}\end{array}$

Therefore, the area of shaded region is is $2\text{sq}\text{.units}$ .