Question

Show that|z-3/z+3|=2 represent a circle

Answer 1

Answer:

This is the equation of a circle with centre at (-5,0) and radius 4 units

Step-by-step explanation:

We have,

Z-3 z+3 = 2

= |z – 3| - 2|z + 3| (x – 3)+ y2 =

Let z x+iy, where x, y ER x + iy - 3 = 2 x + iy + 3

= |(x – 3) + iy 2|(x + 3) + iy|

2/(x+3)2 + y2

+ (x – 3) + y2 4[(x + 3)2 + y2

→ x + 9 - 2 6х + у?

4 [x? + 9+ 6x + y²] → x? +9 – 6x + y?

=

4x2 + 36 + 24 x

+ 4y? = 3x? + 3y? + 30x + 27 = 0 → x? + y2 + 10x + 9=0

This is the equation of a circle with centre at (-5,0) and radius 4 units

Answer 2

Answer:

z+3/z-3=2 ok

Thank You