complex number q (1 Viewer)

[skepticality]

this is out of the patel book

Show that the locus of a point represented by the complex number z = x+ yi and obeying the considion |z-z₁|=3|z-z₂| is a circle. find its center and radius

thanks in advance

 

[icycloud]

Let z₁ = x₁ + iy₁
z₂ = x₂ + iy₂

Then you get (x-x₁)² + (y-y₁)² = 9[(x-x₂)² + (y-y₂)²]

Expand and you get the equation of a circle,

Centre ( [9x₂ - x₁]/8, [9y₂ - y₁]/8)
Radius = Sqrt[(x₁-9x₂)² + (y₁-9y₂)² - 72x₂²+72y₂²-8x₁²-8y₁²]/8

Hmm... you're usually given what z₁ and z₂ is???

 

[skepticality]

Hmm... you're usually given what z₁ and z₂ is???

ye, not this one thgh

 

[klaw]

Let z₁ = x₁ + iy₁
z₂ = x₂ + iy₂

Then you get (x-x₁)² + (y-y₁)² = 9[(x-x₂)² + (y-y₂)²]

Expand and you get the equation of a circle,

Centre ( [9x₂ - x₁]/8, [9y₂ - y₁]/8)
Radius = Sqrt[(x₁-9x₂)² + (y₁-9y₂)² - 72x₂²+72y₂²-8x₁²-8y₁²]/8

Hmm... you're usually given what z₁ and z₂ is???

wow that's messy