IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

ashish_banga

if ${x}^{2} - 3xy + \lambda{y}^{2} + 3x - 5y + 2 = 0$ represents a pair of straight lines and $\theta$ is the angle between them, then cosec^2 $\theta$ is equal to

amitp91

$\theta$ = sin^-1 2 under root h²-ab divided by under root (a-b)² +4h²

a=1 , b =gamma , h= 3

therefore theta = 2 under root 9- gamma dived by under root gamma² + 36

there fore sin theta =2 under root 9- gamma dived by under root gamma² + 36

cosec theta = under root gamma² + 36 divided by 2 under root 9 - gamma

cosec² theta =(under root gamma

²

+ 36 divided by 2 under root 9 - gamma)²

ashish_banga

ANSWER GIVEN IS 10

ananth_patri

we have the formula for angle between the pair of st lines as tan^-1( root over h^2-ab)/a+b.......now apply th t and get the angle then find cosec^2 @....hope u got it.......~cheers

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