The locus of the orthocentre of the triangle formed by the lines (1+p) x-p y+p(1+p)=0 , (1+q) x-q y+q(1+q)=0 and y=0 , where p q , is

Step-by-step solution

Given, lines are (1+p) x-p y+p(1+p)=0 and (1+q) x-q y+q(1+q)=0 On solving Eqs. (i) and (ii), we get C p q,(1+p)(1+q) Equation of altitude C M passing through C and perpendicular to A B is x=p q Slope of line (ii) is ( 1+q q ) . Slope of altitude B N (as shown in figure) is -q 1+q . Equation of B N is y-0= -q 1+q (x+p) y= -q (1+q) (x+p) 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 x=p q and y=-p q h=p q and k=-p q h+k=0 Locu