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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