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Consider family of circles which are passing through the point $(− 1, 1)$ and are tangents to x-axis. If $(h, k)$ are the coordinates of the center of circle then set of values of k is given by the interval

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− 12 ≤ k ≤ 1

k ≤ 12

0 < k < 12

k ≥ 12

answer is D.

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Detailed Solution

Equation of circle

(x − h) 2 + (y − k) 2 = k 2

Substitute point

(− 1, 1)

(− 1 − h) 2 + (1 − k) 2 = k 2

1 + h 2 + 2 h + 1 − 2 k = 0

h 2 + 2 h + (2 − 2 k) = 0

Discriminant

b 2 − 4 a c ≥ 0

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