Question

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

(a) a hyperbola (b) a parabola (c) an ellipse (d) a straight line

Answer 1

Correct option:  (d) a straight line

Explanation:

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

.'. On solving Eq. (iii) and (iv), we get

y = pqand y = -pq + h = pq and k= - pq

h+k=O

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