A) \[{{x}^{2}}+{{y}^{2}}-3x-8y+1=0\]
B) \[{{x}^{2}}+{{y}^{2}}-2x-6y-7=0\]
C) \[2x+4y-9=0\]
D) \[2x+4y-1=0\]
Correct Answer: C
Solution :
Let equation of circle be \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] It passes through (1, 2) i.e. \[1+4+2g+4f+c=0\] and is orthogonal w.r.t\[{{x}^{2}}+{{y}^{2}}=4\]. Therefore, \[2g\times 0+2f\times 0=-c+4\] or \[c=4\] Hence, we get\[2g+4f+9=0\], then\[2x+4y-9=0\] is the required locus.
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