Asosiy tarkibga o'tish

12.4-bo'lim : To'rtburchak yuzalar

3. Quyidagi to'rtburchak sirtni chizing.

\[z = \frac{{{x^2}}}{4} + \frac{{{y^2}}}{4} - 6\]
Yechim

Bu \(z\) o'qi markazida joylashgan elliptik paraboloiddir. \(x\) va \(y\) shartlari ijobiy bo'lgani uchun biz u yuqoriga ochilishini bilamiz. "-6" bizga sirt \(z = - 6\) da boshlanishini aytadi. Yana shuni aytishimiz mumkinki, \(x\) va \(y\) atamalarining koeffitsientlari bir xil bo'lgani uchun sirtning kesmalari aylana bo'ladi.

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 \(z = \frac{{{x^2}}}{4} + \frac{{{y^2}}}{4} - 6\) drawn with the traditional axes. It is a circular paraboloid centered on the z-axis that opens upward with its lowest point at \(z = - 6\), so it looks like a tall bowl.
A three dimensional sketch of the same circular paraboloid \(z = \frac{{{x^2}}}{4} + \frac{{{y^2}}}{4} - 6\), this time drawn with “boxed” axes to make the surface easier to visualize. It opens upward from its lowest point at \(z = - 6\).