Question

equation that represents the set of points that are 5 units from (2, -7).
equation that represents the set of points that are 5 units from (2, -7) is .

Explanation:

Step1: Recall circle standard form

A circle with center $(h,k)$ and radius $r$ has equation:
$$(x-h)^2+(y-k)^2=r^2$$

Step2: Substitute given values

Here, $(h,k)=(2,-7)$ and $r=5$. Substitute these:
$$(x-2)^2+(y-(-7))^2=5^2$$

Step3: Simplify the equation

Simplify the signs and radius squared:
$$(x-2)^2+(y+7)^2=25$$

Answer:

$\boldsymbol{(x-2)^2+(y+7)^2=25}$