Chapter A5.1, Problem 1E

To determine

To find: an equation for the circle and sketch the circle

Answer to Problem 1E

The equation of the circle is:

  $x^2+{\left(y-2\right)}^2=4$

The sketch of the circle is:

  

Explanation of Solution

Given:

  $C\left(0,2\right),a=2$

Calculation:

The equation for a circle is given as-

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

Where,

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

  $a$ is radius of the circle.

Center $=\left(0,2\right)$

Radius $=2$

Therefore equation becomes,

  $\begin{array}{l}{\left(x-0\right)}^2+{\left(y-2\right)}^2=2^2\\ x^2+{\left(y-2\right)}^2=4\end{array}$

Following is the sketch of the circle-

  

Conclusion:

The equation of the circle is:

  $x^2+{\left(y-2\right)}^2=4$

The sketch of the circle is: