If the equation 12x² - 10xy + 2y² + 14x - 5y + k = 0 represents a pair of straight lines, find k, find separate equation and also angle between them.

Find the combined equation of the straight lines whose separate equations are x - 2y - 3 = 0 and x + y + 5 = 0.

A line passing through the points (a, 2a) and (-2, 3) is perpendicular to the line 4x+3y+ 5 = 0, find the value of a.

Find the angle between the pair of straight lines given by
(a² - 3b²)x² + 8ab xy+(b² -3a²)y² =0.

Transform the equation 3x + 4y + 12 = 0 in to normal form.