The normal drawn to the parabola
\[
y^2=8x
\]
at \((2,4)\) meets the parabola again at the point
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For the parabola
\[
y^2=4ax,
\]
the normal at parameter \(t\) is
\[
y=-tx+2at+at^3.
\]
After obtaining the normal, substitute it into the parabola and use the known point to identify the second point of intersection.