If you define y as a function of x which looks like this: $y(x) = x^2$
You can calculate the distance from the zero-point to any result of this function like this: $d = \sqrt{x^{2} + y^{2}}$ and since we know that y(x) = x2 we can now calculate the distance as following: $d = \sqrt{x^{2} + x^{4}}$ or $d^{2} = x^{2} + x^{4}$. Is there a way to solve this eqation by $x$ in order to calculate $x$ using the distance? Am I just blind or is this not that simple or even impossible to solve?
I know some algebra, some trigonometry a tiny little bit of complex stuff but try not to simplify too much I'd love to learn more about things in math :)
Since $d\ge 0$ we have
$$d = \sqrt{x^{2} + x^{4}} \iff x^4+x^2-d^2=0$$
which is a quadratic equation in $x^2$ therefore, keeping only the positive root
$$x^2=\frac{-1+ \sqrt{1+4d^2}}{2} \implies \ldots$$