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 :

• A. \(2\sqrt2\)
• B. 5
• C. \(4\sqrt2\)
• D. 4

Answer 1

The Correct Option is D

The center coordinates are: \[ (2, 1) \]

The circle's equation is: \[ (x - 2)^2 + (y - 1)^2 = 1 \]

The distance QC is calculated as: \[ QC = \sqrt{(5 - 2)^2 + (5 - 1)^2} = 5 \]

The shortest distance, RQ, is found by subtracting CR from CQ: \[ RQ = CQ - CR = 5 - 1 = 4 \]