Determine the projection of the surface 𝑥23−𝑦2=𝑧 on the xy-plane? (Hint: 𝑧=0)Group of answer choicesEllipseHyperbolaOne LineTwo Lines
Question
Determine the projection of the surface 𝑥23−𝑦2=𝑧 on the xy-plane? (Hint: 𝑧=0)Group of answer choicesEllipseHyperbolaOne LineTwo Lines
Solution
To find the projection of the surface 𝑥²3−𝑦²=𝑧 on the xy-plane, we set 𝑧=0 (as per the hint).
So, we have 𝑥²3−𝑦²=0.
This equation can be rewritten as (x/√3)² - y² = 0.
This is the equation of a hyperbola in the xy-plane. Therefore, the projection of the given surface on the xy-plane is a hyperbola.
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