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# Classify this quadric equation watch

1. Hello,

I need classify the following equation in affine space
I think this means to give the type of surface it is...

Im not sure how to go about doing this... I am aware of the matrix representation of such equations... maybe I could use Gauss Jordan on it and simplify the equations?

Im really not sure

Any ideas relating to this?
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2. (Original post by number23)
Hello,

I need classify the following equation in affine space
I think this means to give the type of surface it is...

Im not sure how to go about doing this... I am aware of the matrix representation of such equations... maybe I could use Gauss Jordan on it and simplify the equations?

Im really not sure

Any ideas relating to this?
not my field of expertise

but I think this is a hyperboloid of two sheets shifted (if you complete the square in z)
its axis of symmetry is the z axis and is shifted up this axis by 1
3. (Original post by TeeEm)
not my field of expertise

but I think this is a hyperboloid of two sheets shifted (if you complete the square in z)
its axis of symmetry is the z axis and is shifted up this axis by 1
thanks for the response
how did you come to that answer?
4. (Original post by number23)
thanks for the response
how did you come to that answer?
just facts i.e. that is the standard form of a hyperboloid of two sheets

it is like saying how can you tell (x-2)2+(y-2)2 =4 represents a circle

x2/a2 - y2/b2 -z2/c2 = 1

is a hyperboloid of 2 sheets with axis of symmetry the x axis

think of a 2D hyperbola rotated fully in the x axis
5. (Original post by TeeEm)
just facts i.e. that is the standard form of a hyperboloid of two sheets

it is like saying how can you tell (x-2)2+(y-2)2 =4 represents a circle

x2/a2 - y2/b2 -z2/c2 = 1

is a hyperboloid of 2 sheets with axis of symmetry the x axis

think of a 2D hyperbola rotated fully in the x axis
ok cheers, i didnt think of completing the square bit anyways

im going to learn the equations tbh
6. (Original post by number23)
ok cheers, i didnt think of completing the square bit anyways

im going to learn the equations tbh
note that after you complete the square you move x and y bit to the "z side" to leave the 1 positive.

your hyperboloid is symmetrical in the z axis and translated down the z axis by 1.

good luck

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