Chapter 13.7, Problem 1PSA

(a)

To determine

To write:The equation of circle and find area.

Answer to Problem 1PSA

The equation of circle is $x^2+y^2=5^2$ and the area of the circle is $25\pi$ .

Explanation of Solution

The radius of circle is calculated as,

  $\begin{array}{c}r=\sqrt{x^2+y^2}\\ =\sqrt{3^2+4^2}\\ =5\end{array}$

The general equation of circle is given by,

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

Here, $\left(h,k\right)$ is the centre of the circle.

From the figure the centre of the circle is $\left(0,0\right)$ .

Substitute the values in the above expression.

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

The area of the circle is calculated as,

  $\begin{array}{c}A=\pi r^2\\ =\pi {\left(5\right)}^2\\ =25\pi \end{array}$

Therefore, the equation of circle is $x^2+y^2=5^2$ and the area of the circle is $25\pi$ .

(b)

To determine

To find: The circumference of the circle.

Answer to Problem 1PSA

The circumference of the circle is $10\pi$ .

Explanation of Solution

The circumference of the circle is calculated as,

  $\begin{array}{c}C=2\pi r\\ =2\pi \left(5\right)\\ =10\pi \end{array}$

Therefore, the circumference of the circle is $10\pi$ .