The magnitude of the gradient of the tangent at an extremity of latera recta of the hyperbola `x^2/(a^2)-y^2/(b^2)=1` is equal to (where e is the eccentricity of the hyperbola)

The eccentricity of the hyperbola x^(2)-y^(2)=9 is

Show that the acute angle between the asymptotes of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a^2> b^2), is 2cos^(-1)(1/e), where e is the eccentricity of the hyperbola.

Show that the acute angle between the asymptotes of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a^2> b^2), is 2cos^(-1)(1/e), where e is the eccentricity of the hyperbola.

Eccentricity of the hyperbola x^(2) - y^(2) = a^(2) is :

The eccentricity of the hyperbola x^2-y^2=4 is

The eccentricity of the hyperbola x ^(2) - y^(2) =25 is

The eccentricity of the hyperbola x ^(2) - y^(2) =25 is

If the slope of a tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is 2sqrt(2) then the eccentricity e of the hyperbola lies in the interval

The eccentricity of the hyperbola 16x^(2)-9y^(2)=1 is The eccentricity of the hyperbola 16x^(2)-9y^(2)=1 is

Show that the acute angle between the asymptotes of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1,(a^(2)>b^(2)), is 2cos^(-1)((1)/(e)) where e is the eccentricity of the hyperbola.