The 1st pricture said there are two standard forms of quadric surfaces, but what is the meaning of these two forms? What is the meaning of translation and rotation?

Explain in detail why they are different.

The 2nd picture shows some examples of quadric surface.

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We will then move to see some quadric surfaces. A quadric surface is the graph of a second-degree equation in three variables x, y, z.The most general such equation is given by Ax2 + By2 + Cz2 + Dxy + Eyz+ Fxz+ Gx + Hy +Iz +J= 0, where A, B,C,... ,J are constants, but by translation and rotation it can be brought into one of the two standard forms as below: Ax? + By2 + Cz² + J = 0 Ax2 + By2 + Iz = 0. or Before we look at some quadric surfaces, let us recall some basic facts about circles, ellipses, hyperbolas. y 4 米米 a 9- The red graph above is a circle with radius r whose called an The red graph above is called a ellipse (a hyperbola whose equation is hyperbola whose equation is The red graph above is The red graph above is called a equation is given by x2 + y2 = r2. distorted circle) whose given by given by 2. 2. 21 21 equation is given by 2. %3D 31. 31. 2. =1. The two black dotted lines The two black dotted lines above above are given by +. are given by 2. 2. y PS HDMI Ultra %3D We will then move to see some quadric surfaces. A quadric surface is the graph of a second-degree equation in three variables x, y, z.The most general such equation is given by Ax2 + By2 + Cz2 + Dxy + Eyz+ Fxz+ Gx + Hy +Iz +J= 0, where A, B,C,... ,J are constants, but by translation and rotation it can be brought into one of the two standard forms as below: Ax? + By2 + Cz² + J = 0 Ax2 + By2 + Iz = 0. or Before we look at some quadric surfaces, let us recall some basic facts about circles, ellipses, hyperbolas. y 4 米米 a 9- The red graph above is a circle with radius r whose called an The red graph above is called a ellipse (a hyperbola whose equation is hyperbola whose equation is The red graph above is The red graph above is called a equation is given by x2 + y2 = r2. distorted circle) whose given by given by 2. 2. 21 21 equation is given by 2. %3D 31. 31. 2. =1. The two black dotted lines The two black dotted lines above above are given by +. are given by 2. 2. y PS HDMI Ultra %3D

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Quadric surfaces Quadratic equations and quadric surfaces Planes are examples of flat objects and they are represented by linear equations in a cartesian coordinate system In such a coordinate system ... View the full answer