If the pair of lines joining the origin to the points of intersection of the curve
\[
2x^2-5xy-3y^2-10x+27y-8=0
\]
and the straight line
\[
ax+y=1
\]
are perpendicular to each other and \(a\) is not an integer, then \(a=\)
Show Hint
If two lines through the origin have slopes \(m_1\) and \(m_2\), then they are perpendicular iff
\[
\boxed{m_1m_2=-1.}
\]
Use Vieta's formulas to express \(x_1+x_2\) and \(x_1x_2\) while eliminating the intersection points.