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

Solve this Question and post your answer with solution.

Answer 2) k ≥ 1⁄2

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.