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Find and identify the traces of the quadric surface x2 + y2 − z2 = 36 given the plane. x = k Find the trace. Incorrect: Your answer is incorrect. Identify the trace. circle ellipse hyperbola parabola y = k

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luisongonz

Answer:

Hyperbola.

Step-by-step explanation:

We start from the function:

[tex]x^{2} +y^{2} -z^{2} =36[/tex]

We may get the traces if we cut the surface in planes x=k. This is equivalent to replace x for k:

[tex]k^{2}+y^{2} -z^{2}=36\\y^{2} -z^{2}=36-k^{2}[/tex]

The last equation is the equation of an hyperbola, which varies its characteristics depending on K (the plane cut).