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The locus of the centre of a circle which touches two given circles of different radii externally is 
Asked by ankitraj875725 | 29 Nov, 2018, 15:54: PM
answered-by-expert Expert Answer
Let A and B are the given two circles with radii R1 and R2 respectively and their centres are F and G respectively.
Let C and D are variable circles so that each circle meet the given circles A and B externally.
Let r1 be the radius of circle C and P be its centre. Let r2 be the radius of circle D and Q be its centre.
 
PF = R1+r1  ,  PG = R2+r1 ,   PF-PG = R1 - R2
 
QF = R1+r2  ,  QG = R2+r2 ,  QF-QG = R1 - R2
 
Hence locus of centres of touching circles is  set of points so that the difference between the distances from two given
fixed points ( here F and G ) to the point in locus is  constant.
 
This locus is hyperbola and the fixed points F and G (Centers of given circles ) are foci of hyperbola
Answered by Thiyagarajan K | 30 Nov, 2018, 10:01: AM

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