Ans: A
Since $a > 0 $, then sketch the below graph according to the question.
Since $a > 0 $, then sketch the below graph according to the question.
Since $QR$ lies on the $y$-axis, then the orthocentre must lies on the $x$-aixs. Therefore, $(10,0)$ is the orthocentre.
Note that $P=(\dfrac{a}{2}, 0)$ and $Q = (0, \dfrac{a}{5})$. Let $R = (0,r)$ and $K = (10,0)$. Since $K$ is the orthocentre, then we have
$\begin{array}{rcl}
m_{RK} \times m_{PQ} & = & -1 \\
\dfrac{0-r}{10 – 0} \times \dfrac{\frac{a}{5} – 0}{0 – \frac{a}{2}} & = & -1 \\
\dfrac{-r}{10} \times \dfrac{-2}{5} & = & -1 \\
r & = & -25
\end{array}$
Therefore, the $y$ coordinate of $R$ is $-25$.
