Find the equation of the conicoid

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In summary, the equation of the conicoid 2x^2-y^2=z^2+2x-7, when the origin is shifted to (2,-2,0) and the axes are rotated so that the new axes have direction ratios -1,0,1;1,-2,1;0,1,1, can be found by applying the transformation equations for shifting the origin and rotating the axes. These equations can be used to determine the new coefficients of the equation, which will result in a new equation of the conicoid with the shifted and rotated origin.
  • #1
debrajr
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Find the equation of the conicoid
\(\displaystyle 2x^2-y^2=z^2+2x-7\)
when the origin is shifted to
\(\displaystyle (2,-2,0)\)
and the axes are rotated so that the new axes have direction ratios
\(\displaystyle -1,0,1;1,-2,1;0,1,1\)
 
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  • #2
Hello debrajr and welcome to MHB! :D

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FAQ: Find the equation of the conicoid

What is a conicoid?

A conicoid is a three-dimensional geometric shape that is formed by the intersection of a plane and a double cone.

What are the types of conicoids?

The types of conicoids are elliptic, parabolic, and hyperbolic, depending on the shape of the intersection between the plane and the double cone.

How do you find the equation of a conicoid?

The equation of a conicoid can be found by using the general equation of a conicoid and substituting the values of the coefficients and constants based on the type of conicoid and its orientation.

What information is needed to find the equation of a conicoid?

The information needed to find the equation of a conicoid includes the type of conicoid, its orientation, and the coordinates of its center.

What are some real-life applications of conicoids?

Conicoids have various real-life applications, such as in architecture for designing curved structures, in optics for modeling the shape of lenses, and in engineering for creating smooth surfaces in 3D designs.

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