complex numbers (1 Viewer)

[want2beSMART]

show that the locus specified by 3|z-4-4i|=|z-12-12i| is a circle.

what is the radius and centre?

 

[gordo]

to get the eqn letz z = x+iy and expand
us can see that u have 3 times the modulus of z from 4,4i = the modulus of z from 12,12i)
3x4=12

 

[Slidey]

3|z-4-4i|=|z-12-12i|

9([x-4]^2+[y-4]^2)=([x-12]^2+[y-12]^2)

Blah blah.

 

[tempco]

ah 4u... memories. bad ones.

 

[noah]

9[(x-4)^2+(y-4)^2]=(x-12)^2+(y-12)^2

9(x^2+y^2)-72(x+y)+288=(x^2+y^2)-24(x+y)+288

8(x^2+y^2)-48(x+y)=0

8(x^2+y^2)-48(x+y)+144=144

8[(x-3)^2+(y-3)^2]=144

(x-3)^2+(y-3)^2=18

Therefore circle (equation of,)

centre (3,3)
radius 3sqrt(2)

 

[noah]

i can see i'm late

 

[want2beSMART]

cool thanks peoples