I want to parameterize the equation $c^2 = a^2 + b^2 = d^2 + 4 b^2$ but every avenue I go down leads to an equation I can’t solve.
I know $a^2 + b^2 = c^2$ is parameterized by $(2uvk, (u^2 - v^2)k, (u^2 + v^2)k)$ so it should be as simple as:
$(u^2 + v^2)k = (p^2 + q^2)n$
$(uv)k = (2pq)n$
Or some other combination of terms, but I’m still having trouble actually solving it.
Could anyone provide some guidance?