In y = ax +b when are a, -b/a, b in arithmetic progression. The
polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2
and c be in arithmetic progression?

The illustration shows the graphs of twelve functions. Three of
them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations
of all the other graphs.

Grid Points on Hyperbolas

Age 16 to 18 Challenge Level:

Find a condition which determines whether the hyperbola
$y^2 - x^2 = k$ contains any points with
integer coordinates.