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.

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

Find the equation of the circle which has its centre on the line y = 2 and which passes through the points (2, 0) and (4,0).

Find the equations to the straight lines which are at a distance of 3 unit from the origin and which pass through the intersection of the lines 4x+3y+1=0 and 5x-y=13

Find the equations to the straight lines which are at a distance of 2 unit from the origin and which pass through the point of intersection of the lines 3x+4y=4 and 2x+5y+2=0 .

The equation of the plane through the intersection of the planes x+2y+3z-4=0 and 4x+3y+2z+1=0 and passing through the origin is (a) 17x+14y+11z=0 (b) 7x+4y+z=0 (c) x+14+11z=0 (d) 17x+y+z=0

Find the equation of the diameter of the circle x^(2) + y^(2) - 4x + 6y + 9 = 0 which passes through the point (1, -2).

Thet equations to the sides of a triangle are x-3y=0,4x+3y=5 and 3x+y=0. Then the line 3x-4y=0 passes through the-

Show that the circle x^(2) + y^(2) + 4(x+y) + 4 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x+y+2 = 0 and which also passes through the origin.

Find the equation of the line which is parallel to 3x-2y+5=0 and passes through the point (5,-6) .

Show that the circle x^(2) + y^(2) + 6(x-y) + 9 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x-y+4 = 0 and which also passes through the origin.