x² + y² = r²
Given a point: r² = distance²
Axes: y=0 or x=0
Line meets circle: sub & solve
2 = chord · 1 = tangent · 0 = miss
Tangent slope m_t = -a/b
Sub point into x²+y², compare r²
< inside · = on · > outside
(x-h)² + (y-k)² = r²
Read centre off the brackets (mind signs)
Diameter: centre = midpoint
Symmetry/translation: radius stays, centre moves