A) \[{{x}^{2}}+{{y}^{2}}-2xy+8x+8y-16=0\]
B) \[{{x}^{2}}+{{y}^{2}}-2xy+8x+8y=0\]
C) \[{{x}^{2}}+{{y}^{2}}+8x+8y-16=0\]
D) \[{{x}^{2}}-{{y}^{2}}+8x+8y-16=0\]
Correct Answer: A
Solution :
\[SP\,=PM\Rightarrow \,S{{P}^{2}}=P{{M}^{2}}\] Þ \[{{x}^{2}}+{{y}^{2}}={{\left( \frac{x+y-4}{\sqrt{2}} \right)}^{2}}\] Þ \[{{x}^{2}}+{{y}^{2}}-2xy+8x+8y-16=0.\]
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