Important points about Circle

These are following important points about circle in geometry :

- Equation of circle having center at (0, 0) and radius r :
x

^{2}+y^{2}=r^{2} - Equation of circle having center at (h, k) and radius a :
(x-h)

^{2}+(y-k)^{2}=a^{2} - Standard equation of circle is x
^{2}+y^{2}+2gx+2fy+c=0 where radius=?(g^{2}+f^{2}-c) and center at(-g, -f) and condition is g^{2}+f^{2}-c > = 0 - If g
^{2}+f^{2}-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

S

_{1}=x_{1}^{2}+y_{1}^{2}+2gx_{1}+2fy_{1}+c S_{2}=x_{2}^{2}+y_{2}^{2}+2gx_{2}+2fy_{2}+c - Equation of Circle Passing through point of intersection of circles S
_{1}=0 and S_{2}=0 is S_{1}+kS_{2}=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 S
_{1}=0 and S_{2}=0 intersect then S_{1}-S_{2}=0 is their common chord. - If two circles S
_{1}=0 and S_{2}=0 have internal contact the S_{1}-S_{2}=0 is their internal common tangent. - If Two Circles S
_{1}=0 and S_{2}=0 do not intersect then S_{1}-S_{2}=0 is their radial axis. - If Two Circles S
_{1}=0 and S_{2}=0 have external contact the S_{1}-S_{2}=0 is their external common tangent.

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