Question

An equation that represents the set of points that are 2 units from (-2,-6)

Answer 1

If the set of points have a constant distance (radius, r) from a point, the set of points form a circle, which has the standard equation:

(x-x0)^2+(y-y0)^2=r^2

where (x0,y0) is the given point (-2,-6), and r=radius=2.

Substituting, the equation is then
(x-(-2))^2+(y-(-6))^2=2^2, or

(x+4)^2+(y+6)^2=4......(1)