<s>[INST] Find the Cartesian equation of the locus described by $|z+2-7i| = 2|z-10+2i|$ 
Find the Cartesian equation of the locus described by $|z+2-7i| =
 2|z-10+2i|$ Write your answer in the form $(x+a)^2+(y+b)^2=k$.

This was a question from my end of year exams just gone and I'm unsure as to where I have gone wrong :(. If anyone could point me in the right direction I'd very much appreciate that.
Here was my working:
Let $z = x+iy$
$|z|$ = $\sqrt{x^2+y^2}$
$$|z+2-7i| = 2|z-10+2i| \\
\implies |(x+iy)+2-7i| = 2|(x+iy)-10+2i| \\  
\implies |(x+2)(y-7y)i| = 2|(x-10)+(y+2)i| \\ 
\implies \sqrt{(x+2)^2+(y-7)^2i^2} = 2\sqrt{(x-10)^2+(y+2)^2i^2}  \\
\implies (x+2)^2-((y-7^2) = 2((x-10)^2-(y+2)^2)$$
$$(x^2+4x+4)-(y^2-14y+49) = 2((x^2-20x+100)-(y^2+2y+4)) \\
\implies x^2+4x+4-y^2+14y-49 = 2x^2-40x+200-2y^2-4y-8 \\
\implies -237 = x^2-44x-y^2-18y\\
\implies x^2-44x-y^2-18 = -237$$
 [/INST] Consider z= (x+iy),Now put the value of Z in the given question. 
after applying rules of modulus 
we get `x^2+Y^2-28x+10y+121=0
Now we can arrange in square form like
(x-14)^2+(y+5)^2=45
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