A) \[7x+8y+14=0\]
B) \[7x-8y-14=0\]
C) \[7x-8y+14=0\]
D) \[8x-7y+14=0\]
Correct Answer: B
Solution :
Equations of given circles are \[{{S}_{1}}=2{{x}^{2}}+2{{y}^{2}}-7x=0\] \[\Rightarrow \] \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}-\frac{7}{2}x=0\] and \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}-4y-7=0\] Equation of radical axis is \[{{S}_{1}}-{{S}_{2}}=0\] \[\Rightarrow \]\[\left( {{x}^{2}}+{{y}^{2}}-\frac{7}{2}x \right)-({{x}^{2}}+{{y}^{2}}-4y-7)=0\] \[\Rightarrow \] \[-\frac{7}{2}x+4y+7=0\] \[\Rightarrow \] \[-7x+8y+14=0\] \[\Rightarrow \] \[7x-8y-14=0\]
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