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Q.

For the hyperbola x29y23=1 the incorrect statements are

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a

length of the latusrectum is 2

b

its eccentricity is  43

c

product of the perpendicular distances from any point on the hyperbola on its asymptotes is less than the length of its latusrectum

d

The acute angle between its asymptotes is  π3

answer is B, D.

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Detailed Solution

x29y23=1;9(e21) 
e=23 equation of pair of asymptotes is x29=y23y=±x3
 Angle between asymptotes = π3
Length of L.R. =2b2a=2
Product of perpendicular distance of any point
P(3secθ,3tanθ) from asymptotes
P1P2=|3secθ3tanθ|2|3secθ3tanθ|2 
=94>2 

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