Question

show that |2z+2-4i|=2 represents a circle and find its centre and radius​

Answer 1

Step-by-step explanation:

Solution :

Let z=x+iy. Then,

∣z−3z−2​∣=2

∣(x−3)+iy(x−2)+iy​∣=2

∣(x−2)+iy∣=2∣(x−3)+iy∣

(x−2)2+y2

​=2(x−3)2+y2

​

(x−2)2+y2=4[(x−3)2+y2]

3x2+3y2−20x+32=0

x2+y2−320​x+332​=0

(x−310​)2+(y−0)2=(32​)2, which represents a circle with centre at (310​,0) and radius 32​.