# 2018_Question1_j

First of all, D is the graph y=-x, which is clearly of the form p(y)=-p(x), so we can discount (b) and (e). Also, C is the graph x^2+y^2=r^2 for some r\in\mathbb{R}, and we can write this as (x^2-\frac12r^2)+(y^2-\frac12r^2)=0, so C is also of the desired form, so we can discount (a) too.

We are left to decide between (c) and (d), for which it suffices to decide whether or not A can be written in this form. An important thing to note is that p(x)+p(y)=0 is invariant if we swap x with y, i.e. the graph should have reflective symmetry in the line x=y, and A does not have this, so the answer must be ©.

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