# Challenge 395: Parabola Points

Pin down the minimising point on this parabola!

*P* is the parabola with equation y = x^{2}.

C is the point (0, 1).

X is the point on *P* where the length CX is least, and X' is the point on *P* where the straight line through C and X intersects with *P* again.

Find the ratio CX : CX' in its simplest form.