How do you find the radius of the circle: #x^2 + y^2 + 12x - 2y + 21 = 0#? Precalculus Geometry of an Ellipse Identify Critical Points 1 Answer ali ergin Mar 9, 2016 #r=4# Explanation: #x^2+y^2+D x+E y+F=0# #C(a,b)" coordinates for center of circle"# #a=-D/2" "b=-E/2" "F=21# #x^2+y^2+12x-2y+21=0# #D=12" "E=-2# #a=-12/2=-6" "b=2/2=1# #r=1/2 sqrt(D^2+E^2-4F)# #r=1/2 sqrt(12^2+(-2)^2-4*21)# #r=1/2sqrt(144+4-84)# #r=1/2sqrt64" "r=1/2*8# #r=4# Answer link Related questions How do I find the points on the ellipse #4x^2 + y^2 = 4# that are furthest from #(1, 0)#? What are the foci of an ellipse? What are the vertices of #9x^2 + 16y^2 = 144#? What are the vertices of the graph given by the equation #(x+6)^2/4 = 1#? What are the vertices and foci of the ellipse #9x^2-18x+4y^2=27#? What are the foci of the ellipse #x^2/49+y^2/64=1#? How do I find the foci of an ellipse if its equation is #x^2/16+y^2/36=1#? How do I find the foci of an ellipse if its equation is #x^2/16+y^2/9=1#? How do I find the foci of an ellipse if its equation is #x^2/36+y^2/64=1#? How do you find the critical points for #(9x^2)/25 + (4y^2)/25 = 1#? See all questions in Identify Critical Points Impact of this question 3325 views around the world You can reuse this answer Creative Commons License