X Intercepts And Y Intercepts

Given, lines are
and
C
Equation of altitude CM passing through C and perpendicular to A B is
Slope of line (ii) is
Slope of altitude BN (as shown in frigure) is
Equation of B N is y - 0

Let orthocentre of triangle be H(h, k), which is the point
of intersection of Eqs. (iii) and (iv).
On solving Eqs. (iii) and (iv), we get

and y = -pq

and k = - pq

Locus of H (h , k) is x+ y = 0