Three modes: write the equation from center and radius, expand to general form, or complete the square from general form x²+y²+Dx+Ey+F=0 to find center and radius.
x² + y² + Dx + Ey + F = 0
Standard: (x−h)² + (y−k)² = r²
General: x²+y²+Dx+Ey+F = 0
where h=−D/2, k=−E/2, r=√(h²+k²−F)
Group x and y terms, move F to the right side. Add (D/2)² and (E/2)² to both sides. Factor each group as a perfect square binomial.
A tutor can make completing the square feel natural and help you convert between circle equation forms with confidence.