If the ratio of transverse and conjugate axis of the hyperbola `x^2 / a^2 - y^2 / b^2 = 1` passing through the point `(1, 1)` is `1/3`, then its equation is

The equation of the conjugate axis of the hyperbola x^2/9-(y+2)^2/16=1 is _____

The equation of the conjugate axis of the hyperbola ((x-5)^(2))/(16) -((y-4)^(2))/(9) =1 is

The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is

The conjugate axis of the hyperbola (y-3)^2/9+(x+2)^2/3=1 is parallel to the line x=4.

The equation of the conjugate axis of the hyperbola ((y-2)^(2))/(9)-((x+3)^(2))/(16)=1 is

The equation of the conjugate axis of the hyperbola ((y-2)^(2))/(9)-((x+3)^(2))/(16)=1 is

obtain the equation of hyperbola in each of the following cases: The transverse axis parallel to y-axis the hyperbola passes through the points (11/3,0) , (1,2) and its centre is the intersections of lines x+y-6=0 , 4x-y+1=0.

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is