The vertices of a triangle are \( \left[a t_{1} t_{2}, a\left(t_{1}+t_{2}\right)\right]\left[a t...

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The vertices of a triangle are \( \left[a t_{1} t_{2}, a\left(t_{1}+t_{2}\right)\right]\left[a t_{2} t_{3}, a\left(t_{2}+t_{3}\right)\right],\left[a t_{3} t_{1}, a\left(t_{3}+t_{1}\right)\right] \). Find the coordinates of its orthocentre.
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