Hyperbola `x^2/a^2-y^2/b^2=2` has eccentricity `5/4`. If normal to the hyperbola at `(8/sqrt5,12/5)` is `8sqrt5x+betay=lamda` then the value of `(lamda-beta)` is

The eccentricity of the hyperbola 3x^(2)-4y^(2)=-12 is

The point P(- 2sqrt6, sqrt3) lies on the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 having eccentricity (sqrt5)/2 . If the tangent and normal at P to the hyperbola intersect its conjugate axis at the points Q and R respectively, then QR is equal to :

The eccentricity of the hyperbola (sqrt(2006))/(4) (x^(2) - y^(2))= 1 is

The eccentricity of the hyperbola (sqrt(1999))/(3)(x^(2)-y^(2))=1 , is

The eccentricity of the hyperbola 2x^(2)+3xy-2y^(2)+5=0 is

The eccentricity of the hyperbola 5x ^(2) -4y ^(2) + 20x + 8y =4 is

If the eccentricity of the hyperbola conjugate to the hyperbola (x^2)/(4)-(y^2)/(12)=1 is e, then 3e^2 is equal to:

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3