A) \[x+y=a+b\]
B) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\]
C) \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}-{{b}^{2}}\]
D) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\]
Correct Answer: C
Solution :
\[2\sqrt{{{g}^{2}}-c}=2a\] ?.(i) \[2\sqrt{{{f}^{2}}-c}=2b\] ?.(ii) On squaring (i) and (ii) and then subtracting (ii) from (i), we get \[{{g}^{2}}-{{f}^{2}}={{a}^{2}}-{{b}^{2}}.\] Hence the locus is \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}-{{b}^{2}}\].
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