The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Circle equations and tangents
Connect completed-square and expanded circle equations.
Find circles from a centre, a diameter or sufficient points.
Use the radius–tangent right angle, including exceptional directions.
\((x-a)^2+(y-b)^2=r^2\) has centre \((a,b)\) and radius \(r>0\). Complete both squares; divide by any common coefficient first. A tangent at a point on the circle is perpendicular to the radius. \(r^2=0\) is one point, not a nondegenerate circle.