# Hocus, Pocus, LOCUS!

Geometry Level 3

If the locus of the focus of the variable parabola, which always touches the curve $$C_2$$ : $$x^2=-y$$ at $$(0,0)$$, is $$C_1$$ : $$x^2 + y^2 = 2ay^4$$.

If $$C_1$$ and $$C_2$$ have same length of Latus Rectum and they have no other intersection point, find $$a$$.

Credits: My Mathematics Teacher.

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