*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, \(\displaystyle y=\frac{r}{q}\)

I found the sum of the points of intersection:

\(\displaystyle x=\frac{r-qy}{p}\)

\(\displaystyle a(\frac{r-qy}{p})^2+2hy(\frac{r-qy}{p})+by^2=0\)

\(\displaystyle y^2(aq^2+bp^2-2hpq)+y(2r(hp-aq))+ar^2=0\)

then

\(\displaystyle -\frac{1}{2}\times\frac{2r(hp-aq)}{aq^2+bp^2-2hpq}=\frac{r}{q}\)

works out to

*hq-bp=0*

I can't see where i have gone wrong.

Thanks