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.

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 2/sqrt(3)dot The equation of the hyperbola is a) 2/5(x+2y-3)^2-3/5(2x-y+4)^2=1 b) 2/5(x-y-4)^2-3/5(x+2y-3)^2=1 c) 2/5(2x-y+4)^2-3/5(x+2y-3)^2=1 d) 2(x+2y-3)^2-3(2x-y+4)^2=1

Find the equations of the bisectors of the angles formed by the lines : 3x- 4y + 12 = 0 and 4x + 3y + 2=0.

The equation of a hyperbola conjugate to the hyperbola x^(2)+3xy+2y^(2)+2x+3y=0 is

Find the equation of the bisector of the obtuse angle between the lines 3x-4y+7=0 and 12 x+5y-2=0.

Find the equation of the bisector of the obtuse angle between the lines 3x-4y+7=0 and 12 x+5y-2=0.

Find the equation of the line passing through the intersection of the lines x+2y-3=0 and 4x-y+7=0 and which is parallel to 5x+4y-20=0.

The equation of common tangent to the parabola y^2 =8x and hyperbola 3x^2 -y^2=3 is

Find the equation of the lines passing through the intersection of 3x+4y=7 and x-y+2=0 and with slope : 3.

Find the equation of plane passing through the line of intersection of planes 3x+4y-4=0 and x+7y+3z=0 and also through origin.

The consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals is 11 x + 7y = 9, find the equation of the other diagonal.