Question

Can someone explain level sets and help me figure this question out?

Answer 1

Question:

Answer 2

@wio can you help? been waiting for an hour now for someone to help.

Answer 3

Let \(z=1\) and mess with the equation to try to find out what sort of equation it is.

Answer 4

Also \(z=1\) works as well.

Answer 5

What do you mean by mess with the equation?

Answer 6

Try to get it into a recognizable form.

Answer 7

like \[
ax^2+by^2=c^2
\]This is an ellipse

Answer 8

\[
y=ax^2+bx+c
\]This is a parabola

Answer 9

\[
y=mx+b
\]A line

Answer 10

So the first one: \[
xy+z^2=1\\
\]Well \[
xy=1-z^2
\]And \(1-z^2\) is a constant so:\[
xy=C\implies y=\frac Cx
\]

Answer 11

This is not on the list.

Answer 12

Next one \[
z=\frac{1}{x+y-1}
\] \[
\frac 1z=x+y-1
\] \[
\frac{z+1}{z}=x+y
\]This ends up being: \[
y+x=C\implies y=-x+C
\]This is a line

Answer 13

Since the slope will always be \(-1\) it's parallel lines.

Answer 14

ok I see thanks