Consider a family of circles which are passing through the point (–1, 1) and are tangent to x-axis.(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 .  
−12≤k≤12
B .  
k≤12
C .  
< k < 12
D .  
k≥12
Answer: Option D : D Since, circles are passing through the point (–1, 1) and touching X-axis, the equationof circles can be written as - (h+1)2+(K–1)2=K2 h2+2h+2–2K=0 If h is real the Δ≥0 4- 4.1. (2 – 2K) ≥0 = 4 - 8 + 8k ≥0 = 8k ≥4 = k≥12
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