If the center and radius of the circle | z - 2 z - 3 | = 2 are respectively and , then 3 is equal to [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
If the center and radius of the circle $| \frac{z - 2}{z - 3} |$ $= 2$ are respectively $(α, β)$ and $γ$ , then $3 (α + β + γ)$ is equal to [2023]

1 12

2 11

3 10

4 9

Ans.
(1)

$Centre of circle$ $| \frac{z - a}{z - b} |$ $= k (\neq 1) is$

$(\frac{k^{2} b - a}{k^{2} - 1}, 0)$ and radius = $\frac{k | a - b |}{k^{2} - 1}$

Now, centre of circle $| \frac{z - 2}{z - 3} |$ $= 2$ is $(\frac{4 \times 3 - 2}{4 - 1}, 0)$ i.e., $(\frac{10}{3}, 0)$

and radius = $\frac{2 \times 1}{3} = \frac{2}{3}$ $∴$ $α = \frac{10}{3}, β = 0, γ = \frac{2}{3}$

$3 (α + β + γ) = 3 (\frac{10}{3} + 0 + \frac{2}{3}) = 12$

Want Us to Email you About Special Offers & Updates?