Question

Pls help,

What is the graph of x^2=y^2

Answer 1

\[x^2 = y^2 \iff |x| = |y|\]

Answer 2

But can I treat it as a hyperbola ? x^2-y^2=k

Answer 3

Sure, it's more like \(x^2 - y^2 = 0 \) or \((x + y)(x - y) = 0\)

Answer 4

So if I am required to sketch a 2d trace for a 3d object, which graph do I draw?

Answer 5

Wait, why a 3D object...? You just have to draw two different lines:\[x = y\]and\[x = -y\]

Answer 6

I'd rather treat it as a function, so\[y = x\]and\[y = -x\]are your two different lines.

Answer 7

I am suppose to sketch x^2+y^2/4=z^2

Answer 8

Oh, then a 3D sketch.
I don't really know how to plot 3D, but fortunately http://wolframalpha.com does.

Answer 9

I know haha, but informatively, I have to do it manually by sketching xy plane, xz-plane and yz plane

Answer 10

unfortunately*

Answer 11

Thanks anyway

Answer 12

\[x^2+\frac{y^2}{4}=z^2\]
if \(z=k\) where planes are parallel to the \(xy\)-plane, the graphs are ellipses \[\frac{x^2}{k^2}+\frac{y^2}{4k^2}=1\]