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Prove or disprove: The intersection of the plane [tex]x+y+z=1[/tex] and the cylinder [tex]x^2+y^2=1[/tex] is an ellipse.
A cylindrical section is a shape that is formed by cutting a cylinder along its length. It is essentially a portion of a cylinder with a flat, circular base on one end and a curved surface on the other.
An ellipse is a geometric shape that resembles a flattened circle. It is defined as the set of all points in a plane, the sum of whose distances from two fixed points is constant.
A cylindrical section is essentially an ellipse when viewed from a certain angle. This is because the curved surface of a cylinder can be seen as an ellipse when it is cut and laid flat.
A cylindrical section has two main characteristics that make it an ellipse: a constant sum of distances from two fixed points (foci) and a curved edge that is symmetrical about its center.
Cylindrical sections as ellipses have various applications in engineering and architecture. For example, they are commonly used in the design of bridges, tunnels, and pipes. They can also be seen in the design of satellite dishes and curved mirrors.