A) a hyperbola
B) an ellipse
C) a straight line
D) none of these
Correct Answer: A
Solution :
[a] \[x+iy=1-t+i\sqrt{{{t}^{2}}+t+2}\] |
\[\Rightarrow x=1-t,y=\sqrt{{{t}^{2}}+t+2}\] |
Eliminating t, \[{{y}^{2}}={{t}^{2}}+t+2={{(1-x)}^{2}}+1-x+2={{\left( x-\frac{3}{2} \right)}^{2}}+\frac{7}{4}\] |
\[\Rightarrow {{y}^{2}}-{{\left( x-\frac{3}{2} \right)}^{2}}=\frac{7}{4}\], which is a hyperbola |
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