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 =
Create a free account to view solution
View Solution FreeMore Circle Questions
A circle C1 of unit radius lies in the first quadrant and touches both the co-ordinate axes. The radius of the circle wh...Given an isosceles triangle, whose one angle is 120o and radius of its incircle = √3. Then the area of the triangl...The number of common tangents of the circle x2 + y2 − 2x − 1 = 0 and x2 + y2 − 2y − 7 = 0 is-...The equation of the circle which touches both the axes and the line + = 1 and lies in the first quadrant is (x _ c)2 + (...Let the set of all values of r , for which the circles $(x + 1)^{2} + (y + 4)^{2} = r^{2}$ and $x^{2} + y^{2} - 4x - 2y ...