Question

1. write the standard form of the equation of the circle with the given center and radius. center: (5, -3), r = 4 reference hw 2.8, #13

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify values of $h$, $k$, and $r$

Given that the center is $(5,-3)$, so $h = 5$, $k=-3$, and $r = 4$.

Step3: Substitute values into the formula

Substitute $h = 5$, $k=-3$, and $r = 4$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x - 5)^2+(y+3)^2=16$.

Answer:

$(x - 5)^2+(y + 3)^2=16$