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qr code vb.net open source Surfaces in ThreeSpace in .NET framework
Surfaces in ThreeSpace Code 3 Of 9 Recognizer In .NET Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in .NET framework applications. Code 39 Drawer In .NET Framework Using Barcode encoder for VS .NET Control to generate, create Code 39 image in Visual Studio .NET applications. Figure 1711 Recognizing Code 3 Of 9 In .NET Framework Using Barcode decoder for .NET Control to read, scan read, scan image in .NET framework applications. Print Barcode In Visual Studio .NET Using Barcode creator for VS .NET Control to generate, create barcode image in Visual Studio .NET applications. A hyperboloid of one sheet in Cartesian xyz space, centered at the origin
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Scan Data Matrix In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Make 1D Barcode In C# Using Barcode maker for .NET framework Control to generate, create 1D image in .NET applications. If we make the term containing x2 positive instead of the term containing y2, we get the general equation x2/a2 y2/b2 z2/c2 = 1 which produces a hyperboloid of two sheets whose axis lies along the coordinate x axis, and whose center is at the origin If we move the plus sign so it s in front of the term containing z2, the general equation becomes x2/a2 y2/b2 + z2/c2 = 1 This maneuver gives us a hyperboloid of two sheets whose axis lies along the coordinate z axis, and whose center is at the origin Elliptic cone Figure 1713 shows an elliptic cone It s what we get when we graph an equation of the form x2/a2 + y2/b2 z2/c2 = 0 where a, b, and c are positive realnumber constants The perpendicular cross sections of the cone are always circles or ellipses The cone s axis coincides with the coordinate z axis, and the cone s vertex coincides with the origin The flare angles, as well as the eccentricity of the crosssectional ellipses, depend on the values of a, b, and c Surfaces in ThreeSpace
Figure 1713 An elliptic cone in Cartesian xyz space, centered at the origin
If we move the minus sign so it s in front of the term containing y2, we get the general equation x2/a2 y2/b2 + z2/c2 = 0 whose graph is an elliptic cone with the axis along the coordinate y axis, and whose center is at the origin If we move the minus sign so that it s in front of the term containing x2, the general equation becomes x2/a2 + y2/b2 + z2/c2 = 0 and the graph becomes an elliptic cone whose axis lies along the coordinate x axis, and whose center is at the origin An example Consider the object in Cartesian xyz space represented by
36x2 16y2 + 36z2 = 0 We can divide through by 144 to obtain x2/4 y2/9 + z2/4 = 0 This is the equation for an elliptic cone whose vertex is at the origin, and whose axis coincides with the coordinate y axis Other Surfaces
Another example Consider the object in Cartesian xyz space represented by
x2 + y2 + z2 = 7 When we divide through by 7, we get x2/( 7) + y2/( 7) + z2/( 7) = 1 which simplifies to x2/7 y2/7 z2/7 = 1 This equation describes a hyperboloid of two sheets whose center is at the origin, and whose axis lies along the coordinate x axis Still another example Consider the object in Cartesian xyz space represented by
15x2 + 10y2 = 6z2 + 30 We can subtract 6z2 from each side, getting 15x2 + 10y2 6z2 = 30 Dividing through by 30 gives us x2/2 + y2/3 z2/5 = 1 This is the equation for a hyperboloid of one sheet whose center is at the origin, and whose axis lies along the coordinate z axis

