Chapter 1, Problem 20RE

To determine

To find: the standard form of the equation of the circle

Answer to Problem 20RE

Thus, the standard form of the equation of the circle is ${(x-2)}^2+{(y+4)}^2=9$

Explanation of Solution

Given:

  $\left(h,k\right)=\left(2,-4\right);r=3$

Calculation:

The standard form of an equation of a circle is ${(x-h)}^2+{(y-k)}^2=r^2,$ where $r$ is the radius and $(h,k)$ is the center of the circle.

Substitute the given values

  $\begin{array}{c}{(x-2)}^2+{[y-(-4)]}^2=3^2\\ {(x-2)}^2+{(y+4)}^2=9\end{array}$

Thus, the standard form of the equation of the circle is ${(x-2)}^2+{(y+4)}^2=9$

Conclusion:

Thus, the standard form of the equation of the circle is ${(x-2)}^2+{(y+4)}^2=9$