Question

If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to

• A. 12
• B. 11
• C. 10
• D. 9

Answer 1

Answer: (A)

12

Answer 2

(x−2)2+y2​=2(x−3)2+y2​
=x2+y2−4x+4=4x2+4y2−24x+36
=3x2+3y2−20x+32=0
=x2+y2−320​x+332​=0
=(α,β)=(310​,0)
γ=9100​−332​​=94​​=32​
3(α,β,γ)=3(310​+32​)
=12