MarkFL said:Use the given hint allow with the property of associativity to write:
\(\displaystyle \left(x^2-2xy+y^2 \right)+\left(y^2-2yx+z^2 \right)=0\)
Now do you see how to proceed?
scolon94 said:I'm still confused because of the -2xy and -2yz. Is it possible to complete the square?
A quadric surface is a mathematical term used to describe a three-dimensional shape that can be represented by a second degree equation in three variables (x, y, z). It is a type of 3D surface that can be classified into different categories based on its characteristics.
A quadric surface can be classified by its equation, which can help determine its shape and properties. It can also be classified based on its intersections with the coordinate planes and the types of conics that it contains.
The different types of quadric surfaces include ellipsoids, hyperboloids, paraboloids, cones, and cylinders. These surfaces can further be classified into different categories based on their equations and properties.
Quadric surfaces have several properties, including symmetry, curvature, and intersection with coordinate planes. They also have special properties such as foci, center, and axes of symmetry. These properties can help in classifying and understanding the shape of the surface.
Quadric surfaces are used in many areas of science, including physics, engineering, and computer graphics. They are used to represent real-world objects and phenomena, such as the shape of planets, electromagnetic fields, and 3D models. They also play an important role in the study of conic sections and their applications in science and mathematics.