Inverse Points with Respect to a Circle

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

1. a hyperbola
2. a straight line
3. an ellipse
4. a circle

Q. If $(x_1,y_1)$ and $(x_2,y_2)$ are the extremities of a focal chord of the parabola $3y^2=4x,$ then $x_1{x}_2+y_1{y}_2$ is equal to $\frac{-p}{q}$ where $p,q$ are co-prime. Then value of $q-p$ is

1. $2$
2. $4$
3. $1$
4. $0$

Q. If $(x_1,y_1)$ and $(x_2,y_2)$ are the extremities of a focal chord of the parabola $3y^2=4x,$ then $x_1{x}_2+y_1{y}_2$ is equal to $\frac{-p}{q}$ where $p,q$ are co-prime. Then value of $q-p$ is

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

1. a hyperbola
2. an ellipse
3. a straight line
4. a circle

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

1. a hyperbola
2. an ellipse
3. a straight line
4. a circle