Important points about Circle

These are following important points about circle in geometry :

  1. Equation of circle having center at (0, 0) and radius r :
    x2+y2=r2 
  2. Equation of circle having center at (h, k) and radius a :
    (x-h)2+(y-k)2=a2 
  3. Standard equation of circle is x2+y2+2gx+2fy+c=0 where radius=?(g2+f2-c) and center at(-g, -f) and condition is g2+f2-c > = 0
  4. If  g2+f2-c=0 then equation represents a point circle having center only (-g, -f).
  5. Diametrical form of a circle


    Figure – (X-x)(X-a)+(Y-y)(Y-b) = 0


    S1=x12+y12+2gx1+2fy1+c 
    S2=x22+y22+2gx2+2fy2+c
    
  6. Equation of Circle Passing through point of intersection of circles S1=0 and S2=0 is S1+kS2=0 where k is not equal to -1.
  7. Equation of circle passing through a point of intersection of circle s=0 and line u=0 is s+ku=0
  8. If the circles S1=0 and S2=0 intersect then S1-S2=0 is their common chord.

  9. If two circles S1=0 and S2=0 have internal contact the S1-S2=0 is their internal common tangent.

  10. If Two Circles S1=0 and S2=0 do not intersect then S1-S2=0 is their radial axis.

  11. If Two Circles S1=0 and S2=0 have external contact the S1-S2=0 is their external common tangent.

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