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Position of a Point with Respect to a Circle

Let the circle is x2 + y2 + 2gx + 2fy + c = 0.
 
68671.png
 
Point P lies outside, on or inside the circle accordingly as CP >, =, < radius
 
or 68665.png >, =, < 68659.png
 
or x12 + y12 + 2gx1 + 2fy1 + c >, =, < 0

Maximum and minimum distance of a point from the circle

Let any point P (x1, y1) and circle x2 + y2 + 2gx + 2fy + c = 0.
 
The center and radius of the circle are (–g, –f) and 68653.png respectively. The maximum and minimum distance from P (x1, y1) to the circle (1) are
 
PB = CB + PC = r + PC
 
68647.png
 
and PA = |CPCA| = |PCr| (P inside or outside)
 
where r = 68641.png.

 

Note: If PC < r then P inside, PC > r then P outside.




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