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0 votes
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in Mathematics by (67.9k points)

The area of the parallelogram formed by the tangents at the end of conjugate diameters of an ellipse is

(a)  Constant and is equal to the product of the axes

(b)  Cannot be constant

(c)  Constant and is equal to the two lines of the product of the axes.

(d)  None of these

1 Answer

+1 vote
by (63.3k points)
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Best answer

Correct option  (a) 

Explanation:

Two diameters are said to be conjucgate when each bisects all chords parallel to the other.

Conjugate diameters are diameters passing through centre and product of their slopes is equal to -b2/a2

Area of parallelogram =  4 area of parallelogram

QDCE =  4 (2 area of  ΔCDE)

= 4 (abcos2α + absin2α)

= 4 ab 

= (2a)×(2b)

= Product of the axes of ellipse

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