бірқуысты гиперболоид деп аталады (10-сурет), ал
(23)
теңдеуі арқылы анықталған бет екіқуысты гиперболоид делінеді. (11-сурет).
(24)
теңдеуі анықтайтын бет конус деп аталады (12-сурет).
Тікбұрышты декарттық жүйеде
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(25)
теңдеуі анықтайтын бет эллипстік параболоид деп аталады (13-сурет).
Тікбұрышты декарттық жүйеде
(26)
теңдеуі анықтайтын бет гиперболалық параболоид деп аталады.
(14-сурет).
Кеңістіктегі тікбұрышты декарттық жүйеде
(27)
теңдеуі анықтайтын бет екінші ретті цилиндр деп аталады. хОу жазықтығынды (27) теңдеуі анықтайтын екінші ретті сызық цилиндрдің бағыттауышысы деп аталады. Цилиндр бағыттауышысының кез келген нүктесінен өсіне параллель түзу осы цилиндрдің жасаушысы деп аталады.
Егер бағыттаушысы эллипс болса, цилиндр эллипстік; болса дөңгелек цилиндр ( 15 сурет); гипербола болса, цилиндр гиперболалық (16 сурет); парабола болса, цилиндр параболалық деп аталады (17-сурет).
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