about to only mathematics

Options

A. a hyperbola
B. a parabola
C. an ellipse
D. a straight line

Answer

D

Explanation

The intersection point y=0 with the first line si B(-p, 0).
The intersection point of y=0 with the second line is A(-q, 0).
The intersection point of the two line is
C(pq, (p+1)(q+1)
The altitude from C to AB is x = pq.
The altitude from B to AC is
`y = -(q)/(1+q)(x+p)` Solving these two, we get x=pq and y=-pq.
Therefore, the locus of the orthocenter is x+y=0.