Two sides of a triangle are $y=m_{1}x$ and $y=m_{2}x$ ;  $m_1,m_2$    are  the roots of the equation $x^2+ax-1=0$ .  For all values of ‘a’, the orthocenter of the triangle lies at

$y=m_{1}x$  $y=m_{2}x$ 

                $x^2+ax-1=0$

                $m_1.m_2=-1$

The orthocenter of the right angled triangle is vertex at right angle

since the given triangle is right angled triangle, the point of intersection of perpendicular sides is vertex at right angle, 

and it is orthocentre of the triangle 

therefore, the orthocenter = (0,0)