A) all integral value of K
B) \[0<K<1\]
C) \[K<0\]
D) for two values of K
Correct Answer: D
Solution :
The equation of the circle passing through the point (1, 0), (0, 1) and (0, 0) is \[{{x}^{2}}+{{y}^{2}}-x-y=0.\]This passes through (2K, 3K). Therefore, \[4{{K}^{2}}+9{{K}^{2}}-2K-3K=0\]\[\Rightarrow \]\[13{{K}^{2}}-5K=0\] \[K(13K-5)=0\]\[\Rightarrow \]\[K=0,5/13,\]
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