Equation of circle in Complex Form

Q.

If the line x+2by+7=0 is a diameter of the circle $x^2+y^2-6x+2y=0$, then b=

1. -5

2. -1

3. 5

4. 3

Q.

When $\frac{z+i}{z+2}$ is purely imaginary then z lies on

1. Circle of radius

2. circle of radius

3. straight line

4. parabola

Q.

The centre of the circle $z\overline{z}-(2+3i)z-(2-3i)\overline{z}+9$ = 0 is

1. ( 2, -3 )

2. ( 2, 3 )

3. ( -2, -3 )

4. ( -2, 3 )

Q.

If $|$z$|$ = 3, then the points representing the complex numbers $-2+4z$ lie on a

1. Straight line

2. Circle

3. Ellipse

4. Parabola

Q.

If z lies on the circle $|z-1|=1$, then $\frac{z-2}{z}$ equals

1. 2

2. -1

3. 0

4. None of these

Q.

If $|z-z_1|+|z+z_2|$ = $\lambda ,\lambda \in R^{+},z_1,z_2$ are fixed complex numbers, represents an ellipse, then:

1. 

2. 

3. 

4. 

Q.

If z lies on the circle $|$z$|$ = 1, then $\frac{2}{z}$ lies on

1. - = 2

2. + = 4

3. - = 4

4. - = 8

Q.

If z lies on the circle $|z-1|=1$, then $\frac{z-2}{z}$ equals

1. 0

2. 2

3. -1

4. None of these

Q. The equation $z\overline{z}+a\overline{z}+\overline{a}z+b=0,bϵR$ represents a circle if

1. None of these
2. $|a{|}^2>b$
3. $|a{|}^2=b$
4. $|a{|}^2<b$