Answer
Elliptic Paraboloid
Work Step by Step
\[
x = y^2 + 4z^2
\]
Evaluated at \(x = 0\):
\[
y^2 + 4z^2 = 0 \\
x = 0 \quad \text{and} \quad y = 0
\]
Evaluated at \(x = 4\):
\[
y^2 + 4z^2 = 4 \\
\frac{y^2}{4} + \frac{4z^2}{4} = 1 \\
\frac{y^2}{2^2} + \frac{z^2}{1^2} = 1
\]
Ellipse with radius 1 on \(z\)-axis and 2 on \(x\)-axis.
Another way of solving is that it follows the standard formula of the Elliptic Paraboloid:
\[
\frac{z}{c} = \frac{x^2}{a^2} + \frac{y^2}{b^2}
\]
In this case, the paraboloid is oriented along the \(x\)-axis (instead of the \(z\)-axis as in the standard form).
