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A circle of non-zero radius has origin as its centre. If it passes through the point of intersection of two curves $$y^2 = 4ax$$ and $$x^2 = 4ay$$, then its equation is
Curves $$y^2 = 4ax$$ and $$x^2 = 4ay$$ intersect where $$y(y^3 - 64a^3) = 0$$:
So $$x^2 + y^2 = 32a^2$$.
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