A) \[{{x}^{2}}+{{y}^{2}}+3x-6y-40=0\]
B) \[{{x}^{2}}+{{y}^{2}}+6x-3y-45=0\]
C) \[{{x}^{2}}+{{y}^{2}}+8x+4y-20=0\]
D) \[{{x}^{2}}+{{y}^{2}}+4x+8y+20=0\]
Correct Answer: B
Solution :
Given circle is \[\left( 2,\ \frac{3}{2} \right)\text{ },\ \frac{5}{2}={{r}_{1}}\] (say) Required normals of circlres are \[x+3=0,\ x+2y=0\] which intersect at the centre \[\left( -3,\ \frac{3}{2} \right)\text{ },\ {{r}_{2}}=\]radius (say). 2nd circle just contains the 1st i.e., \[{{C}_{2}}{{C}_{1}}={{r}_{2}}-{{r}_{1}}\Rightarrow {{r}_{2}}=\frac{15}{2}\].
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