Let a tangent \(L_1\) with slope \(m\) drawn to the parabola
\[
y^2=8x
\]
be perpendicular to a normal \(L_2\) drawn to the parabola
\[
y^2=12x.
\]
If \(m=1\) and the point of intersection of \(L_1\) and \(L_2\) is \((\alpha,\beta)\), then \(\alpha+\beta=\)
Show Hint
For the parabola
\[
y^2=4ax,
\]
the tangent with slope \(m\) is
\[
\boxed{y=mx+\frac{a}{m}.}
\]
The normal is obtained from the parametric equation of the parabola.