Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point ( 3 , 2 ) and parallel to the coordinate axes touch it. Then the shortest distance of the circle C

Question

Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point ( 3 , 2 ) and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point ( 5 , 5 ) is :

TestHub · Accepted Answer

Coordinates of the centre will be ( 2 , 1 ) Equation of circle will be ​ ( x − 2 ) 2 + ( y − 1 ) 2 = 1 QC = ( 5 − 2 ) 2 + ( 5 − 1 ) 2 ​ QC = 5 ​ shortest distance ​ = RQ = CQ − CR = 5 − 1 = 4 ​

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