A) xy
B) \[{{x}^{2}}-{{a}^{2}}{{y}^{2}}\]
C) \[\frac{{{x}^{2}}-{{y}^{2}}}{4}\]
D) \[\frac{{{x}^{2}}-{{y}^{2}}}{{{a}^{2}}}\]
Correct Answer: C
Solution :
Given \[f(x+ay,\,x-ay)=axy\] ?..(i) Let \[x+ay=u\] and \[x-ay=v\] Then \[x=\frac{u+v}{2}\] and \[y=\frac{u-v}{2a}\] Substituting the value of x and y in (i), we obtain \[f(u,v)=\frac{{{u}^{2}}-{{v}^{2}}}{4}\] Þ \[f(x,\,y)=\frac{{{x}^{2}}-{{y}^{2}}}{4}\].
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