Úloha ID 748 - 
Velikost vektoru u (4; y) je √65. Bodem A [−2;−1] vedeme přímku m, která je určená vektorem u. Obecná rovnice přímky n je x−2 = 0.
Napište rovnici kružnice, jejíž střed S leží na průsečíku přímek m a n. Osa x je tečnou kružnice.
Správná odpověď je: E
Velikost u (4; y) je √65: 42 + y2 = 65 a vyjde y=7.
Pak tedy můžeme buď sestrojit rovnici přímky m (delší), a nebo zkusit umístit vektor u do bodu A: 4+(−2) = 2, tady vidíme, že pokud přičtu vektor k bodu A, dostanu souřadnicovou osu dva pro x, což je nadějné:
n je x−2 = 0 neznamená nic jiného, než že rovnice x=2 je rovnoběžka s osou y a že hledáme střed S [2; y].
Protože už nám pro x vyšlo dva, pak přičteme ještě Ay k uy a dostaneme −1 + 7 = 6.
Střed S [2;6] pak dává i poloměr (tečna je osa x, tedy poloměr bude 6).
(x − m)2 + (y − n)2 = r2
(x − 2)2 + (y − 6)2 = 62
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