Answer:
when k > 0 the traces parallel to the yz plane is an ellipse
The traces parallel to the xz plane are parabolas and they open in positive x- axis direction
The traces parallel to the xy plane are parabolas that open in the positive x-axis direction
Step-by-step explanation:
Given surface : [tex]x^2 = y^2 + 5z^2[/tex]
To determine the traces of the given equation we will have to make some assumptions and the assumption is
let x = k
[tex]k^2 = y^2 + 5z^2[/tex]
when k > 0 the traces parallel to the yz plane is an ellipse
let y = k
[tex]x^2 = k^2 + 5z^2[/tex]
The traces parallel to the xz plane are parabolas and they open in positive x- axis direction
Let z = k
[tex]x^2 = y^2 + 5k^2[/tex]
The traces parallel to the xy plane are parabolas that open in the positive x-axis direction
with the given traces The surface can be sketched
