Chapter 1, Problem 19RE

To determine

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

Answer to Problem 19RE

Therefore, the standard form of the equation of the circle is ${(x+1)}^2+{(y+2)}^2=1$

Explanation of Solution

Given:

  $\left(h,k\right)=\left(-1,-2\right);r=1$

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 the given values

  ${(x+1)}^2+{(y+2)}^2=1^2$

  ${(x+1)}^2+{(y+2)}^2=1$

Therefore, the standard form of the equation of the circle is ${(x+1)}^2+{(y+2)}^2=1$

Conclusion:

Therefore, the standard form of the equation of the circle is ${(x+1)}^2+{(y+2)}^2=1$