The locus of the orthocenter of the triangle formed bythe lines (+p)x-

1.	The locus of the orthocenter of the triangle formed bythe lines (+p)x-py+ pt)-0 and y 0, where p q, is.l+p)-0, (1q)x-gyg(l
Answer» let the orthocentre be H(h,k)after plotting the line, points on x and y axis are: -q(q +1)/2(p+1),0 and 0,q+1 respectively. Hence the bisector eqn. for sides x = 0 and y = 0 are -----------> x = -q(q +1)/2(p + 1) and y = (q +1)/2 there fore pints of intesection is h,k that is x,yequating and dividing them we get, h/k = -q/(p+1)ory = (-(p+1)/q)x or y = mxwhich is a straight line.

The locus of the orthocenter of the triangle formed bythe lines (+p)x-py+ pt)-0 and y 0, where p q, is.l+p)-0, (1q)x-gyg(l

Answer»

let the orthocentre be H(h,k)after plotting the line, points on x and y axis are:

-q(q +1)/2(p+1),0 and 0,q+1 respectively.

Hence the bisector eqn. for sides x = 0 and y = 0 are ----------->

x = -q(q +1)/2(p + 1) and y = (q +1)/2

there fore pints of intesection is h,k that is x,yequating and dividing them we get,

h/k = -q/(p+1)ory = (-(p+1)/q)x

or y = mxwhich is a straight line.