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Question 35

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 $$y(y^3 - 64a^3) = 0$$:

  • $$(0, 0)$$: trivial, gives degenerate circle.
  • $$(4a, 4a)$$: distance from origin $$= \sqrt{(4a)^2 + (4a)^2} = 4a\sqrt 2$$.

So $$x^2 + y^2 = 32a^2$$.

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