Simple Section

Geometry Level 2

The graph x2+y2=z23x^2 + y^2 = \dfrac{z^2}{3} intersects with the graph z=ky+cz = ky + c, where kk and cc are real numbers, such that the intersected points form a parabola with the point (0,12,32)\left (0 , \dfrac{-1}{2}, \dfrac{\sqrt{3}}{2}\right) as its vertex.

What is the value of k2k^2?

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