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 above
Correct Answer: D
Solution :
\[\frac{3}{ax+iby}-2={{e}^{i\theta }}\] \[\frac{3-2ax-2iby}{ax+iby}={{e}^{i\theta }}\] 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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