A) \[{{(ax-by)}^{2}}-2{{a}^{3}}x-2{{b}^{3}}y+{{a}^{4}}+{{a}^{2}}{{b}^{2}}+{{b}^{4}}=0\]
B) \[{{(ax+by)}^{2}}-2{{a}^{3}}x-2{{b}^{3}}y-{{a}^{4}}+{{a}^{2}}{{b}^{2}}-{{b}^{4}}=0\]
C) \[{{(ax-by)}^{2}}+{{a}^{4}}+{{b}^{4}}-2{{a}^{3}}x=0\]
D) \[{{(ax-by)}^{2}}-2{{a}^{3}}x=0\]
Correct Answer: A
Solution :
\[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{\left( \frac{bx+ay-ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)}^{2}}\] On solving we get \[{{(ax-by)}^{2}}-2{{a}^{3}}x-2{{b}^{3}}y+{{a}^{4}}+{{a}^{2}}{{b}^{2}}+{{b}^{4}}=0\].
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