maths.free › Precalculus › Conic sections

Conic sections

Circles, ellipses, parabolas and hyperbolas as equations and as surfaces sliced.

Slice a cone and you get a circle, an ellipse, a parabola or a hyperbola; algebraically they are the second-degree equations in x and y. Completing the square in each variable reveals the centre and shape. The 3D view draws z = the expression, whose level curve z = 0 is the conic.

工作范例 · x^2 + y^2 - 25

Algebra · Expressions

Analyse x^2 + y^2 - 25

x^{2} + y^{2} - 25

一步

  1. x^{2} + y^{2} - 25

    An expression in x, y. Here is what it does.

发送答案
x^{2} + y^{2} - 25

现在轮到你 选择问题, 输入或绘制您自己的 。 每一步, 图片, 答案隐藏到您询问 。

保持你自己的工作

免费账户在每一课上都添加注解, 记录你完成的, 在一个地方解决的, 以及您可以询问的关于此页的导师。 数学本身向每个人开放, 是否签名 。

签名上签名 登录

此处所用符号

输入完整定义、图片和其中每个字母的含义的符号。

如何: Conic sections

  1. An expression in x, y. Here is what it does.

人们对人们提出的问题

What is a function, really?

A rule that assigns exactly one output to each input. The vertical-line test on a graph is the same idea: no input may have two outputs.

Why do we need complex numbers?

Because x² + 1 = 0 has no real solution, and allowing one new number i with i² = −1 makes every polynomial equation solvable. They then turn out to describe rotation, waves and alternating current more naturally than real numbers do.

更多 Precalculus

Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremVectorsExponential and logarithmic functionsPolynomial division and the remainder theoremParametric equations and polar coordinates