A) \[{{x}^{2}}+{{y}^{2}}+10xy=0\]
B) \[{{x}^{2}}+{{y}^{2}}+5xy=0\]
C) \[2{{x}^{2}}+2{{y}^{2}}+5xy=0\]
D) \[2{{x}^{2}}+2{{y}^{2}}-5xy=0\]
Correct Answer: C
Solution :
Equation of pair of tangents is given by\[S{{S}_{1}}={{T}^{2}}\]. Here \[S={{x}^{2}}+{{y}^{2}}+20\text{ }(x+y)+20,\ \ {{S}_{1}}=20\] \[T=10(x+y)+20\] \[\therefore \ S{{S}_{1}}={{T}^{2}}\] \[\Rightarrow 20\,\{{{x}^{2}}+{{y}^{2}}+20(x+y)+20\}={{10}^{2}}{{(x+y+2)}^{2}}\] \[\Rightarrow 4{{x}^{2}}+4{{y}^{2}}+10xy=0\Rightarrow 2{{x}^{2}}+2{{y}^{2}}+5xy=0\].
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