A) \[2ax+2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
B) \[2ax+2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
C) \[2ax-2by+({{a}^{2}}+{{b}^{2}}+4)=0\]
D) 2ax \[2ax-2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
Correct Answer: A
Solution :
Let the equation of circle be \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] ?.(i) Circle (i) cuts the circle \[{{x}^{2}}+{{y}^{2}}=4\] orthogonally. \[\therefore \] \[2g0+2f0=c-4\] \[\Rightarrow \] \[c=4\] Also circle (i) passes through (a,b). \[\therefore \] \[{{a}^{2}}+{{b}^{2}}+2gx+2fb+4=0\] Now, locus of centre \[(-g,-f)\] is \[2ax+2by-({{a}^{2}}+{{b}^{2}}+4)=0\]
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