The line passing through the extremity A of the major axis and extremity B of the minor axis of t...

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Counter-Strike: Source
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Counter-Strike: Source (2004)
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The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2+9 y^2=9 meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is
(A) 31/10
(B) 29/10
(C) 21/10
(D) 27/10
The normal at a pointon the ellipse x^2+4 y^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 point
(A) (±3 √(5)/2, ±2/7)
(B) (±3 √(5)/2, ±√(19)/4)
(C) (± 2 √(3), ±1/7)
(D) (± 2 √(3), ±4 √(3)/7)
In a triangle A B C with fixed base B C, the vertex A moves such that cos B+cos C=4 sin ^2A/2.
If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then
(A) b+c=4 a
(B) b+c=2 a
(C) locus of point A is an ellipse.
(D) locus of point A is a pair of straight lines.

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