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Algebra

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 Joined: 19 Aug 2008 Post: 8684
20 Sep 2011 13:15:41 IST
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Maths Challenging Question For IIT aspirants
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

Hey Folks,

This is a challenging Maths question for all of you.  So lets see who solves it first.

Question) Consider a family of circles which are passing through the point (−1, 1) and are tangent to x- axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

(a) 0 < k < 1⁄2
(b) k ≥ 1⁄2
(c) − 1⁄2 ≤ k ≤ 1⁄2
(d) k ≤ 1⁄2

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Joined: 19 Aug 2008
Posts: 8684
20 Sep 2011 16:41:29 IST
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anyone solved this question??????

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Joined: 19 Aug 2008
Posts: 8684
21 Sep 2011 08:46:41 IST
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Solution:-

Equation of circle (x − h)2 + (y − k)2 = k2
It is passing through (− 1, 1) then
(− 1 − h)2 + (1 − k)2 = k2
h2 + 2h − 2k + 2 = 0
D≥0
2k − 1 ≥ 0 ⇒ k ≥ 1/2.

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28 Feb 2012 09:36:48 IST
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New kid on the Block

Joined: 15 Sep 2011
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7 Apr 2012 11:10:52 IST
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Easy !!

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