A) ellipse if \[a=1,\,\,b=2\]
B) circle if \[a=b=1\]
C) pair of straight line if \[a=1,\,\,b=0\]
D) All of them
Correct Answer: D
Solution :
\[\frac{3}{ax+i\,by}-2={{e}^{i\theta }}\]\[\frac{3-2ax-2iby}{ax+i\,\text{by}}={{e}^{i\theta }}\] Take modulus both sides \[{{(3-2ax)}^{2}}+4{{b}^{2}}{{y}^{2}}={{a}^{2}}{{x}^{2}}+{{b}^{2}}{{y}^{2}}\] When \[a=1\] and \[b=2\] then\[\frac{{{(x-2)}^{2}}}{1}+\frac{{{y}^{2}}}{1/4}=1\]which is an ellipse When \[a=b=1\] then circle. When \[a=1\] and \[b=2\] then\[{{x}^{2}}-4x+3=0\]represent pair of straight line.
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