I've tried to solve this problem:
Find an equation of the parabola with vertex at point $(1,1)$ whose directrix is the line $x-2y=6$. It has to be solved using translation and rotation (coordinate transformation).
Any ideas?
2026-04-11 23:01:38.1775948498
Equation of a parabola: Translations and rotation
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Hint: Imagine that you are dealing with the “normal” parabola with vertex at $(1,1)$, namely the one whose directrix is $x=1$. Then ask yourself by what angle does $x=1$ have to be rotated, so as to be parallel to $x=2y+6$. Then apply the rotation matrix corresponding to that particular angle to the algebraic equation of the afore-mentioned parabola.