Check whether the conicoid central or not

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SUMMARY

The discussion focuses on determining whether the conicoid defined by the equation $$3x^2-5y^2+z^2-6xy+7yz=15$$ is central. If it is central, the center and the conics resulting from the intersection with the coordinate planes must be identified. If not, the task is to find all tangent planes that are parallel to the coordinate planes. The user is encouraged to share their progress to facilitate effective assistance.

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Check whether the conicoid represented by
$$3x^2-5y^2+z^2-6xy+7yz=15$$
is central or not.

If it is central, obtain the center and the conics given by the intersection of the conicoid with the coordinate planes.

If the given conicoid is not central, obtain all its tangent planes parallel to the coordinate planes.
 
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Hello debrajr and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

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