A) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=4{{R}^{2}}{{x}^{2}}{{y}^{2}}\]
B) \[{{({{x}^{2}}+{{y}^{2}})}^{3}}=4{{R}^{2}}{{x}^{2}}{{y}^{2}}\]
C) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=4{{R}^{2}}{{x}^{2}}{{y}^{2}}\]
D) \[({{x}^{2}}+{{y}^{2}})(x+y)={{R}^{2}}xy\]
Correct Answer: B
Solution :
Slope of \[AB=\frac{-h}{k}\] |
Equation of AB is \[hx+ky={{h}^{2}}+{{k}^{2}}\] |
\[A\left( \frac{{{h}^{2}}+{{k}^{2}}}{h},0 \right)B\left( 0,\frac{{{h}^{2}}+{{K}^{2}}}{k} \right)\] |
As, \[A=2R\] |
\[\Rightarrow \] \[({{h}^{2}}+{{k}^{2}})=4{{R}^{2}}{{h}^{2}}{{k}^{2}}\]\[\Rightarrow \] \[({{x}^{2}}+{{y}^{2}})=4{{R}^{2}}{{x}^{2}}{{y}^{2}}.\] |
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