Your work out is correct.
One of the medians of the triangle formed by the line pair and the line lies along the y-axis. If neither a nor r is zero, prove that bp+hq=0.
The line pair has its vertex at (0,0), so that is the vertex of the median on the y-axis. Then the midpoint of the intersection of the line pair and the line would be the other point on the median and triangle.
When x=0, on the line,
I found the sum of the points of intersection:
works out to hq-bp=0
I can't see where i have gone wrong.