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

Options

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

Explanation

To find the locus of the orthocenter of the triangle formed by the given lines and the x-axis, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Lines**:
The equations of the lines are:
\[
(1+p)x - py + p(1+p) = 0 \quad \text{(Line 1)}
...