<s>[INST] Finding the locus in terms of a and b Find the locus of the point equidistant from $(a+b,b-a)$ and $(a-b,a+b)$ 
Okay so I don't know how do I find the locus of the point in terms of $ a$ & $b $.
 [/INST] Let $(x,y)$ be a point on the locus. Then:
$$(x-(a+b))^2+(y-(b-a))^2=(x-(a-b))^2+(y-(a+b))^2$$
Expanding:
$$x^2-2x(a+b)+(a+b)^2+y^2-2y(b-a)+(b-a)^2=x^2-2x(a-b)+(a-b)^2+y^2-2y(a+b)+(a+b)^2$$
$$-2y(b-a)+2y(a+b)=2x(a+b)-2x(a-b)$$
$$4ya=4xb$$
$$y=\frac{b}{a}x$$
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