IIT-JEE Exam

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??

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IIT-JEE Other Question

(A) If -1 < x < 1, then f(x) satisfies (p) 0 < f(x) < 1
(B) If 1 < x < 2, then f(x) satisfies (q) f(x) < 0
(C) If 3 < x < 5, then f(x) satisfies (r) f(x) > 0
(D) If x > 5, then f(x) satisfies (s) f(x) < 1 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?