Rectangle Meets Parabola

Geometry Level 3

Suppose \(OABC\) is a rectangle where \(O\) is the origin and vertices \(A\) and \(C\) lie on the parabola \(\displaystyle y = x^2\). On which of the following parabolas must point \(B\) lie?

Note: Assume that the rectangle lies in the \(xy\)-plane.

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