A) \[x+y+1=0\]
B) \[x+y-1=0\]
C) \[x-y-1=0\]
D) \[x-y+1=0\]
Correct Answer: D
Solution :
Given, equation of circles are \[{{S}_{1}}\equiv {{x}^{2}}+{{y}^{2}}+4x+7=0\] and \[{{S}_{2}}\equiv 2{{x}^{2}}+2{{y}^{2}}+3x+5y+9=0\] or \[{{S}_{2}}\equiv {{x}^{2}}+{{y}^{2}}+\frac{3}{2}x+\frac{5}{2}y+\frac{9}{2}=0\] Equation of radical axis\[{{S}_{1}}-{{S}_{2}}=0\] \[\Rightarrow \] \[({{x}^{2}}+{{y}^{2}}+4x+7)\] \[-\left( {{x}^{2}}+{{y}^{2}}+\frac{3}{2}x+\frac{5}{2}y+\frac{9}{2} \right)=0\] \[\Rightarrow \] \[\left( 4-\frac{3}{2} \right)x-\frac{5}{2}y+7-\frac{9}{2}=0\] \[\Rightarrow \] \[\frac{5}{2}x-\frac{5}{2}y+7-\frac{9}{2}=0\] \[\Rightarrow \] \[x-y+1=0\]
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