Question

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

Answer 1

Answer:

Hyperbola.

Step-by-step explanation:

We start from the function:

$x^{2} +y^{2} -z^{2} =36$

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

$k^{2}+y^{2} -z^{2}=36\\y^{2} -z^{2}=36-k^{2}$

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