# Simple Section

Geometry Level 2

The graph $$x^2 + y^2 = \dfrac{z^2}{3}$$ intersects with the graph $$z = ky + c$$, where $$k$$ and $$c$$ are real numbers, such that the intersected points form a parabola with the point $$\left (0 , \dfrac{-1}{2}, \dfrac{\sqrt{3}}{2}\right)$$ as its vertex.

What is the value of $$k^2$$?

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