A) \[{{x}^{2}}+2by={{b}^{2}}+{{a}^{2}}\]
B) \[{{x}^{2}}-2by={{b}^{2}}+{{a}^{2}}\]
C) \[{{x}^{2}}+2by={{a}^{2}}-{{b}^{2}}\]
D) \[{{x}^{2}}-2by={{b}^{2}}-{{a}^{2}}\]
Correct Answer: C
Solution :
Here \[2\sqrt{{{g}^{2}}-c}=2a\Rightarrow {{g}^{2}}-{{a}^{2}}-c=0\].....(i) and it passes through (0, b), therefore \[{{b}^{2}}+2fb+c=0\] ?.(ii) On adding (i) and (ii), we get \[{{g}^{2}}+2fb={{a}^{2}}-{{b}^{2}}\] Hence locus is \[{{x}^{2}}+2by={{a}^{2}}-{{b}^{2}}\] .
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