Find the equation of the hyperbola, whose asymptotes are the straight lines `(x + 2y + 3) = 0, (3x + 4y + 5) = 0` and which passes through the point (1-1).

Find the equation of the hyperbola whose asymptotes are 3x=+-5y and the vertices are (+-5,0)

Find the equation of a hyperbola whose asymptotes are 2x - y- 3 = 0 and 3x + y - 7 = 0 and which pass through (1, 1).

What is the equation of the straight line parallel to 2x+3y+1=0 and passes through the point (-1, 2) ?

Find the equation of the line drawn through the point of intersection of the lines x-2y+3=0 and 2x-3y+ 4=0 and passing through the point (4,-5).

The asymptotes of a hyperbola having centre at the point (1, 2) are parallel to the lines 2x + 3y = 0 " and " 3x + 2y = 0 . If the hyperbola passes through the point (5, 3) show that its equation is (2x + 3y - 8) (3x + 2y + 7) = 154 .