If e is the eccentricity of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` and `theta` is the angle between the asymptotes, then `cos.(theta)/(2)` is equal to

If the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=-1 is (5)/(4) , then b^(2) is equal to

The angle between the asymptotes of the hyperbola xy= a^2 is

The angle between the asymptotes of the hyperbola x^(2)//a^(2)-y^(2)//b^(2)=1 is

Let P(theta_1) and Q(theta_2) are the extremities of any focal chord of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose eccentricity is e. Let theta be the angle between its asymptotes. Tangents are drawn to the hyperbola at some arbitrary points R. These tangent meet the coordinate axes at the points A and B respectively. The rectangle OABC (O being the origin) is completedm, then Q. If cos^(2)((theta_1+theta_2)/(2))=lambdacos^(2)((theta_1-theta_2)/(2)) , then lambda is equal to

The angle between the asymptotes of the hyperbola x^(2) -3y^(2) =3 is

The angle between the asymptotes of the hyperbola x^(2) -3y^(2) =3 is

The angle between the asymptotes of the hyperbola 3x^(2)-y^(2)=3 , is

Let P(theta_1) and Q(theta_2) are the extremities of any focal chord of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose eccentricity is e. Let theta be the angle between its asymptotes. Tangents are drawn to the hyperbola at some arbitrary points R. These tangent meet the coordinate axes at the points A and B respectively. The rectangle OABC (O being the origin) is completedm, then Q.Locus of point C is

The angle between the asymptotes of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is equal to

The angle between the asymptotes of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is equal to