Asosiy tarkibga o'tish

12.4-bo'lim : To'rtburchak yuzalar

1. Quyidagi to'rtburchak sirtni chizing.

\[\frac{{{y^2}}}{9} + {z^2} = 1\]
Yechim

Bu \(x\) o'qi markazida joylashgan silindr. Tsilindrning kesmalari ellips bo'ladi.

Eslatmalarda berilgan tenglamalarni boshqa koordinata o'qlariga "tarjima" qilishingiz mumkinligiga ishonch hosil qiling. Koordinatalar o'qlaridan birida markazlashganda ular qanday ko'rinishini bilganingizdan so'ng, oddiy va bashorat qilinadigan o'zgaruvchan o'zgarishlar ularni boshqa koordinata o'qlarida markazlashtiradi.

Bu erda mintaqaning bir nechta eskizlari. Biz ularga an'anaviy o'qlarni, shuningdek, sirtni tasavvur qilish uchun "qutili" boltalarni berdik.

A three dimensional sketch of the surface \(\frac{{{y^2}}}{9} + {z^2} = 1\) drawn with the traditional axes. It is an elliptic cylinder lying along the x-axis, with an elliptical cross section that is 3 units across in the y direction and 1 unit in the z direction.
A three dimensional sketch of the same elliptic cylinder \(\frac{{{y^2}}}{9} + {z^2} = 1\), this time drawn with “boxed” axes to make the surface easier to visualize. It lies along the x-axis with an elliptical cross section that is wider in the y direction than it is tall in the z direction.