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Given $z=1-t+i\sqrt{t^2+t+2}$ wher $t$ is a real parameter.The locus of z in Argand plane is

$\begin{array}{1 1}(A)\;\text{Circle}&(B)\;\text{Parabola}\\(C)\;\text{Ellipse}&(D)\;\text{Hyperbola}\end{array} $

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$z=x+iy=1-t+i\sqrt{t^2+t+2}$
$x=1-t\Rightarrow t=1-x$
$y^2=t^2+t+2$
$\;\;\;\;=(1-x)^2+(1-x)+2$
$\Rightarrow y^2=x^2-3x+4$
$\Rightarrow$ Locus of z is hyperbola
Hence (D) is the correct answer.
answered Apr 10, 2014 by sreemathi.v
 

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