The profit Rs.y accumulated in thousand in x months is given by y = -x²  + 10x - 15. Find the best time to end the project.

Show that the given lines 3x - 4y - 13 = 0, 8x - 11y = 33 and 2x - 3y - 7 = 0 are concurrent and find the concurrent point.

For what value of k does 2x² + 5xy + 2y² + 15x + 18y + k = 0 represent a pair of straight lines.

The slope of one of the straight lines ax² + 2hxy + by² = 0 is twice that of the other, show that 8h² = 9ab.

For what values of a and b does the equation (a - 2)x² + by² + (b - 2)xy + 4x + 4y - 1 = 0 represents a circle? Write down the resulting equation of the circle.