Chapter 1, Problem 17RE

To determine

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

Answer to Problem 17RE

The standard form of the equation of the circle is ${(x+2)}^2+{(y-3)}^2=16$

Explanation of Solution

Given:

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

Calculation:

The standard form of the equation of a circle with center $(h,k)$ and radius $r$ is given by

  ${(x-h)}^2+{(y-k)}^2=r^2$

Substitute -2 for h, 3 for k, and 4 for $r$

  ${(x+2)}^2+{(y-3)}^2=4^2$

  ${(x+2)}^2+{(y-3)}^2=16$

Therefore, the standard form of the equation of the circle is ${(x+2)}^2+{(y-3)}^2=16$

Conclusion:

Therefore, the standard form of the equation of the circle is ${(x+2)}^2+{(y-3)}^2=16$