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Solution


Q.

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:          [2024]
1 22  
2 42  
3 4  
4 5  

Ans.

(3)

Centre of circle = (2, 1)

∴   Equation of circle will be

(x – 2)2 + (y – 1)2 = 1

Distance between C(2, 1) and P(5, 5)

= (2 – 5)2 + (1 – 5)2

= 5 units

Also, AC = BC = 1 unit               [∵   Radius = 1]

∴   Shortest distance of circle from P = 5 – 1 = 4 units.