The equation of the transverse and conjugate axes of a hyperbola are, respectively, `x+2y-3=0 and 2x-y+4=0,` and their respective lengths are `sqrt2` and `2//sqrt3`. The eqaution of the hyperbola is

The equation of the transvers and conjugate axes of a hyperbola are, respectively, x+2y-3=0 and 2x-y+4=0 , and their respective lengths are sqrt(2) and 2sqrt(3)dot The equation of the hyperbola is 2/5(x+2y-3)^2-3/5(2x-y+4)^2=1 2/5(x-y-4)^2-3/5(x+2y-3)^2=1 2(2x-y+4)^2-3(x+2y-3)^2=1 2(x+2y-3)^2-3(2x-y+4)^2=1

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.

Find the asymptotes and axes of hyperbola having equation xy-3y-4x+7=0 .

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

If normal at P to a hyperbola of eccentricity 2 intersects its transverse and conjugate axes at Q and R, respectively, then prove that the locus of midpoint of QR is a hyperbola. Find the eccentricity of this hyperbola

The length of the transverse axis of the hyperbola 9x^(2)-16y^(2)-18x -32y - 151 = 0 is

Find the equation of the ellipse whose axes are of length 6 and 2sqrt(6) and their equations are x-3y+3=0 and 3x+y-1=0 , respectively.

The equation of the transvers axis of the hyperbola (x-3)^2+(y=1)^2+(4x+3y)^2 is x+3y=0 (b) 4x+3y=9 3x-4y=13 (d) 4x+3y=0

The equation of conjugate axis of the hyperbola x y-3y-4x+7=0 is (a) y+x=3 (b) y+x=7 (c) y-x=3 (d) none of these

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