Q.

The line passing through the extremity A of the major axis and extremi ty B of the minor axis of the ellipse x2+9y2=9 meets its auxiliary circle at the point MThen the area of the triangle with vertices at A, M, and O (the origin) is.

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a

2710

b

3110

c

2910

d

2110

answer is A.

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Detailed Solution

The equation of line AM isx+3y−3=0 Perpendicular distance of line from the origin =310 Length of AM=29−910=2×910 or Area =12×2×910×310=2710 sq. units.
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The line passing through the extremity A of the major axis and extremi ty B of the minor axis of the ellipse x2+9y2=9 meets its auxiliary circle at the point MThen the area of the triangle with vertices at A, M, and O (the origin) is.