Show that the equation 12x² - 10xy + 2y² + 14x - 5y + 2 = 0 represents a pair of straight lines and also find the separate equations of the straight lines.

Find the equation of the circle passing through the points (0, 1) , (4 ,3) and (1, -1).

As the number of units produced increases from 500 to 1000 and the total cost of production increases from. Rs 6000 to Rs 9000. Find the relationship between the cost (y) and the number of units produced (x) if the relationship is linear.

Find whether the points (-1,-2), (1,0) and (-3, -4) lie above, below or on the line 3x + 2y + 7 = 0.

Find the axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)² = 4(x - 1).