Find all solutions to the equation $\displaystyle x^2 + 2y^2 = w^2$ with x>0, y>0, w>0.

I have several problems similar to this one and I do not understand how to do them. The chapter focuses on pythagorean tripes of $\displaystyle a^2 + b^2 = c^2$ but I can not figure out how to apply that when there are additional parts to the equation.