Important points about Circle
These are following important points about circle in geometry :
- Equation of circle having center at (0, 0) and radius r :
- Equation of circle having center at (h, k) and radius a :
- 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
- If g2+f2-c=0 then equation represents a point circle having center only (-g, -f).
- Diametrical form of a circle
Figure – (X-x)(X-a)+(Y-y)(Y-b) = 0
- 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.
- Equation of circle passing through a point of intersection of circle s=0 and line u=0 is s+ku=0
- If the circles S1=0 and S2=0 intersect then S1-S2=0 is their common chord.
- If two circles S1=0 and S2=0 have internal contact the S1-S2=0 is their internal common tangent.
- If Two Circles S1=0 and S2=0 do not intersect then S1-S2=0 is their radial axis.
- If Two Circles S1=0 and S2=0 have external contact the S1-S2=0 is their external common tangent.