JEE Main | 2014CircleHard

Question

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to

Options

A.
B.
C.
D.

Solution

       
C ≡ (x -1)2 +(y -1)2 = 1
Radius of T = |y|
T touches C externally
(0 - 1)2 + (y - 1)2 = (1 + |y|)2
⇒     1 + y2 + 1 - 2y = 1 + y2 + 2|y|
If y > 0,
y2 + 2 - 2y = y2 + 1 + 2y
⇒     4y = 1
⇒     y =
If y < 0,
y2 + 2 - 2y = y2 + 1 - 2y
⇒     1 = 2 (Not possible)
∴     y =

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