A) Only one value of k
B) \[0<k<1\]
C) \[k<0\]
D) All integral values of k
Correct Answer: A
Solution :
[a] The equation of the circle through (1, 0), (0, 1) and (0, 0) is \[{{x}^{2}}+{{y}^{2}}-x-y=0\]it passes through \[(2k,3k)\] So, \[4{{k}^{2}}+9{{k}^{2}}-2k-3k=0\]or \[13{{k}^{2}}-5k=0\] \[\Rightarrow \,\,\,\,k(13k-5)=0\Rightarrow k=0\] or \[k=\frac{5}{13}\] But \[k\ne 0\][\[\because \] all the four points are distinct] \[\therefore k=\frac{5}{13}.\]
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