The equation of the transverse and conugate axes of a hyperbola are respectively`3x+4y-7=0 and 4x-3y+8=0` and their respective lengths are 4 and 6. Find the equation of the hyperbola.

Find the foci of the hyperbola 9x^2-4y^2=36 .

The length of the transverse axis of the hyperbola 4 x^(2)-9 y^(2)+8 x+40=0

The length of transverse axis of the hyperbola 3x^(2) - 4y^(2) = 32 is

Find the equation of the plane with the intercept 2,3 and 4 on x,y and z axes respectively.

The length of the transverse axid , along x - axis with centre at origin of a hyperbola is 7 and it passes through the point (5,-2) . The equations of the hyperbola is :

The equation of the tangent to the hyperbola 4 y^(2)=x^(2)-1 at the point (1,0) is

The eccentricity of the hyperbola with asymptotes 3 x+4 y=2 and 4 x-3 y+5=0 is

Find the equation of the line which cuts off intercepts 7 and -4 on x and y-axes respectively.

If a hyperbola passes through a focus of the ellipse (x^(2))/(25)+(y^(2))/(16) =1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse and the product of their eccentricities is 1, then the equation of hyperbola is