Let `z=1-t+isqrt(t^2+t+2)`, where `t` is a real parameter.the locus of the z in argand plane is

Options

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

Answer

A

Explanation

`x+iy=1-t+isqrt(t^(2)+t+2)`
`rArr " " x=1-t, y=sqrt(t^(2)+t+2)`
Eliminating t,
`y^(2)=t^(2)+t+2=(1-x)^(2)+1-x+2=(x-(3)/(2))^(2)+(7)/(4)`
`rArr " " y^(2)-(x-(3)/(2))^(2)=(7)/(4)`, which is a hyperbola