Question

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

• A. a hyperbola
• B. an ellipse
• C. a straight line
• D. none of these

Answer 1

The correct option is A a hyperbola

$x=1-t$ and $y=\sqrt{(1+t{)}^2+1}$
Hence
$t=(1-x)$
Now
$y^2=(1+t{)}^2+1$
$=(1+1-x{)}^2+1$
$y^2-(x-2{)}^2=1$
Hence this resembles a Hyperbola.