If 2a $$-$$ 5b $$-$$ 3c = 0, show that the straight line ax + by + c = 0 always passes through a fixed point. Find the equation of one straight line passing through this fixed point and parallel to the line 9x + 12y = 20.

The equations to the pairs of opposite sides of a parallelogram are x² $$-$$ 5x + 6 = 0 and y² $$-$$ 6y + 5 = 0. Find the equations of its diagonals.

Find the image of the point ($$-$$8, 12) with respect to the line 4x + 7y + 13 = 0.