G6.4 A straight line with slope $=-2$ passes through the origin cutting the curve at two points $E$ and
$F$. If $\frac{7}{s}$ is the $y$-coordinate of the midpoint of $E F$, find the value of $s$.
$$
\begin{array}{l}
\text { Sub. } y=-2 x \text { into } y=-2 x^{2}+5 x-2 \\
-2 x=-2 x^{2}+5 x-2 \\
2 x^{2}-7 x+2=0
\end{array}
$$

Let $E=\left(x_{1}, y_{1}\right), F=\left(x_{2}, y_{2}\right)$.
$$
\begin{array}{l}
x_{1}+x_{2}=\frac{7}{2} \\
\frac{7}{s}=\frac{y_{1}+y_{2}}{2}=\frac{-2 x_{1}-2 x_{2}}{2}=-\left(x_{1}+x_{2}\right)=\frac{7}{-2} \\
s=-2
\end{array}
$$