Center (-1, 3) and tangent to the line y=2

Step-by-step explanation:

Standard form of the equation of a circle:  (x−h)2+(y−k)2=r2  

Where (h,k) is the center of the circle and r is the radius.

The center is given, just need to find the radius. A tangent line is given, and the radius drawn to the tangent point is perpendicular to the tangent line. Since the tangent line is horizontal the radius is vertical and the length can be counted. (If the tangent line was not horizontal or vertical, then a different method would be used (distance formula).) In this case the radius is 1. Thus the equation of the circle is:

(x+1)2+(y−3)2=1