CircleEasy
Question
Consider a family of circles which are passing through the point (-1, 1) and are tangent to xaxis. 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
Options
A.0 < k < 1/2
B.k ≥ 1/2
C.- 1/2 ≤ k ≤ 1/2
D.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.
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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