- #1
JeffNYC
- 26
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In general, say:
we have a surface: y^2/4 - x^2/3 - z^2 = 1
I know that this is a hyperboloid of 2 sheets, since the xz trace:
x^2/3 + z^2 =-1 doesn't exist,
But for the other traces:
xy trace: y^2/4 - x^2/3 = 1 and yz trace: y^2/4 - z^2 = 1
Which are both hyperbolas - how do I sketch these? What should I be looking at in the 2 equations:
xy trace: y^2/4 - x^2/3 = 1 and yz trace: y^2/4 - z^2 = 1
...to help me understand where they are positioned on the graph (intercepts, vertices, etc...)
Thanks,
Jeff
we have a surface: y^2/4 - x^2/3 - z^2 = 1
I know that this is a hyperboloid of 2 sheets, since the xz trace:
x^2/3 + z^2 =-1 doesn't exist,
But for the other traces:
xy trace: y^2/4 - x^2/3 = 1 and yz trace: y^2/4 - z^2 = 1
Which are both hyperbolas - how do I sketch these? What should I be looking at in the 2 equations:
xy trace: y^2/4 - x^2/3 = 1 and yz trace: y^2/4 - z^2 = 1
...to help me understand where they are positioned on the graph (intercepts, vertices, etc...)
Thanks,
Jeff