# Focus of parabola using only a ruler

It is an easy exercise that using ruler and compass one find the focus of a given parabola.

Can one do the same using only a ruler? -- if not, why?

• Is this for a ruler or a straightedge and compass? – Random832 Dec 31 '14 at 20:22
• @Random832: yes, perhaps, but i don't know -- my native languages are Russian, Maths and "things-as-they-are". But if you talk about en.wikipedia.org/wiki/Straight_edge then i agree! – Victor Jan 1 '15 at 6:13

• Assume that there is some construction on the plane $\pi$ which given parabola $\gamma$ gives its focus $F$. Let $T$ be projective map for which $T(\gamma)$ is a parabola again, but $T(F)$ is not it's focus. Apply the same construction to $T(\gamma)$ on $T(\pi)$, we get $T(F)$. Contradiction. – Fedor Petrov Apr 28 '16 at 8:35