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← JEE Main 2015 · 10 Apr · Shift 1
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JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 62

The largest value of r for which the region represented by the set {ω∈C/∣ω−4−i∣≤r}\{\omega\in\mathbb C/|\omega-4-i|\le r\} is contained in the region represented by the set {z∈C/∣z−1∣≤∣z+i∣}\{z\in\mathbb C/|z-1|\le|z+i|\}, is equal to :

Choose one option
Answer and worked solution

Official answer: D

∣z−1∣≤∣z+i∣|z-1|\le|z+i| is the half-plane on the side of the perpendicular bisector of 1 and −i-i, the line y=−xy=-x, that contains 1: x+y≥0x+y\ge0.

The disc about 4+i4+i must stay inside it, so rr is at most the distance from (4,1)(4,1) to x+y=0x+y=0:
r=52=522.r=\frac{5}{\sqrt2}=\frac52\sqrt2.

Topics:Geometry in the complex planeDistance of a point from a line
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