Question

(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 81 given the plane. x = k Find the trace.

Answer 1

Answer:

Hyperbola

Step-by-step explanation:

Consider $x=k.$

Substitute $x=k$ in given equation $x^2+y^2-z^2=81$

$k^2+y^2-z^2=81$

$\Rightarrow y^2-z^2=9^2-k^2$

$\Rightarrow y^2-z^2=(9-k)(9+k)$

Here, different orientation for $-9$ then $-9$ or $k$

Hence, the surface equation represents a trace of the hyperbola.