Points A (-3, -2), B (-6, a), C (-3, -4) and D(0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.

The vertices of a triangle are (5, 1), (11, 1) and (11, 9). Find the co-ordinates of the circumcentre of the triangle.

Given A = (x + 2, -2) and B = (11, 6). Find x if AB = 17.

The centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 units.