If a hyperbola passing through the origin has `3x-4y-1=0` and `4x-3y-6=0` as its asymptotes, then find the equation of its transvers and conjugate axes.

Find the equation of the hyperbola which has 3x-4y+7=0 and 4x+3y+1=0 as its asymptotes and which passes through the origin.

The equation of the line passing through the centre of a rectangular hyperbola is x-y-1=0 . If one of its asymptotoes is 3x-4y-6=0 , the equation of the other asymptote is

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.

An ellipse passes through the point (4,-1) and touches the line x+4y-10=0. Find its equation if its axes coincide with the coordinate axes.

The equation of transverse axis of hyperbola (passing through origin) having asymptotes 3x-4y=1 and 4x-3y=6 is ax+by-c=0, ,a, b in N and g, c, d(a, b, c)=1 then the value of a+b+c is

A hyperbola passes through (2,3) and has asymptotes 3x-4y+5=0 and 12x+5y-40=0 .Then,the equation of its transverse axis is 77x-21y-265=021x-77y+265=021x-77y-265=021x+77y-265=0

Statement 1: The asymptotes of hyperbolas 3x+4y=2 and 4x-3y=5 are the bisectors of the transvers and conjugate axes of the hyperbolas.Statement 2: The transverse and conjugate axes of the hyperbolas are the bisectors of the asymptotes.

The asymptotes of a hyperbola are 3x-y-7=0 and x-5y-3=0. The hyperbola passes through the point (2,1) . Find the equation of the hyperbola and its centre.

A hyperbola passes through (1,2) and has asymptotes as x+y-2=0 and 7x+y-8=0 .Eccentricity of the hyperbola is equal