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Question

4(xy+2)2+9(x+y4)2=25 represents an ellipse whose :

A
eccentricity is 53
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B
Length of major axis is 52
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C
Length of latus rectum is 1029
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D
Center is (1,3)
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Solution

The correct options are
A eccentricity is 53
B Length of major axis is 52
C Length of latus rectum is 1029
D Center is (1,3)
xy+2=0 and x+y4=0 are perpendicular lines
Let
xy+22=X and x+y42=Y

4(2X)2+9(2Y)2=25

X2258+Y22518=1

a2=258, b2=2518
Center of ellipse is the point of intersection of xy+2=0 and x+y4=0 that is (1,3)

e2=1b2a2 (as a>b)
=1818=1018=59
e=53
Length of major axis is 2a=2×522=52
Length of latus rectum
=2b2a=2×2518×225=1029

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