# When does this happen?

Geometry Level pending

Consider a parabola $$y^{2}=4ax$$ with $$a>0$$. Points $$A, B, C$$ with coordinates $$( x_{i}, y_{i} )$$, where $$i={1,2,3}$$, respectively, on the parabola are such that orthocenter of the triangle $$ABC$$ is the focus of the parabola.

Find the value of $$\left( \dfrac{y_{1}}{2a} -1\right) \left( \dfrac{y_{2}}{2a} -1\right)\left( \dfrac{y_{3}}{2a} -1\right)$$.

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