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Q.

The area (in sq.units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse x29+y25=1, is

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a

274

b

27

c

18

d

272

answer is D.

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Detailed Solution

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Given ellipse x29+y25=1 e=23 one end of latusrectum(L)=2, 53 equation  of Tangent at L is x(2)9+y(5/3)5=1 2x9+y3=1  

The tangents drawn at the end of the laterarecta to the ellipse will intersect at the x and the y axis because of symmetry. The area of the quadrilateral thus formed will be 4 times the area of the triangle formed by the tangent and the coordinate axes

Area of quadrilateral=4(1229×13)                                        =27

 

 

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