Question

Show that the equation represent a circle, and find its centre and radius. |3z − 2 − i| = 3

Answer 1

Answer:

Let z=x+iy. Then,

∣

z−3

z−2

∣=2

∣

(x−3)+iy

(x−2)+iy

∣=2

∣(x−2)+iy∣=2∣(x−3)+iy∣

(x−2)

2

+y

2

=2

(x−3)

2

+y

2

(x−2)

2

+y

2

=4[(x−3)

2

+y

2

]

3x

2

+3y

2

−20x+32=0

x

2

+y

2

−

3

20

x+

3

32

=0

(x−

3

10

)

2

+(y−0)

2

=(

3

2

)

2

, which represents a circle with centre at (

3

10

,0) and radius

3

2

.