# Check whether or not the conicoid represented by #5x^2+4y^2-4yz+2xz+2x-4y-8z+2=0# is central or not. If it is, transform the equation by shifting the origin to the center. Else, change any one coefficient to make the equation that of a central conicoid.?

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See below.

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I hope it helps.

can be represented as

with

After solving by making

which represents the conicoid center.

From the matrix

which is a hyperboloid of two sheets added to a plane.

Describe your changes (optional) 200