Find the eccentricity of the hyperbola with asymptotes `3x+4y=2` and `4x-3y=2.`

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 eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is 2 (b) 2sqrt(3) (c) 4 (d) 4/5

Find the centre, foci and eccentricity of the hyperbola 12x^(2)-4y^(2)-24x+32y-127=0

Find the eccentricity of the conic 4(2y-x-3)^2-9(2x+y-1)^2=80

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

Find the eccentricity, centre, foci and vertices of the hyperbola 5x^(2)-4y^(2)=20 .

Find the lengths of the major and minor axes and the eccentricity of the ellipse ((3x-4y+2)^2)/(16)+((4x+3y-5)^2)/9=1

The equation of a rectangular hyperbola whose asymptotes are x=3 and y=5 and passing through (7,8) is x y-3y+5x+3=0 x y+3y+4x+3=0 x y-3y+5x-3=0 x y-3y+5x+3=0

lf the eccentricity of the hyperbola x^2-y^2(sec)alpha=5 is sqrt3 times the eccentricity of the ellipse x^2(sec)^2alpha+y^2=25, then a value of alpha is : (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

Find the eccentricity, centre, foci and vertices of the hyperbola 9x^(2)-16y^(2)-18x-64y-199=0 .