IIT-JEE Exam

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?

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IIT-JEE Other Question

The normal at a point P on the ellipse x^2 + 4y^2 = 16 meets the x-axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectums of the given ellipse at the points?? A line with positive direction cosines passes through the point P(2, - 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ
equals??