Match each equation with its name.
-
a
b
c
d
e
(
x
2
)
2
+
(
y
4
)
2
+
(
z
2
)
2
=
1
\displaystyle {\left(\frac{{x}}{{2}}\right)}^{{2}}+{\left(\frac{{y}}{{4}}\right)}^{{2}}+{\left(\frac{{z}}{{2}}\right)}^{{2}}={1}
(
2
x
)
2
+
(
4
y
)
2
+
(
2
z
)
2
=
1
-
a
b
c
d
e
(
x
2
)
2
+
(
y
4
)
2
=
z
2
\displaystyle {\left(\frac{{x}}{{2}}\right)}^{{2}}+{\left(\frac{{y}}{{4}}\right)}^{{2}}=\frac{{z}}{{2}}
(
2
x
)
2
+
(
4
y
)
2
=
2
z
-
a
b
c
d
e
(
x
2
)
2
−
(
y
4
)
2
+
(
z
2
)
2
=
0
\displaystyle {\left(\frac{{x}}{{2}}\right)}^{{2}}-{\left(\frac{{y}}{{4}}\right)}^{{2}}+{\left(\frac{{z}}{{2}}\right)}^{{2}}={0}
(
2
x
)
2
−
(
4
y
)
2
+
(
2
z
)
2
=
0
-
a
b
c
d
e
(
x
2
)
2
−
(
y
4
)
2
=
z
2
\displaystyle {\left(\frac{{x}}{{2}}\right)}^{{2}}-{\left(\frac{{y}}{{4}}\right)}^{{2}}=\frac{{z}}{{2}}
(
2
x
)
2
−
(
4
y
)
2
=
2
z
-
a
b
c
d
e
(
x
2
)
2
−
y
4
+
(
z
2
)
2
=
0
\displaystyle {\left(\frac{{x}}{{2}}\right)}^{{2}}-\frac{{y}}{{4}}+{\left(\frac{{z}}{{2}}\right)}^{{2}}={0}
(
2
x
)
2
−
4
y
+
(
2
z
)
2
=
0
elliptic paraboloid on y axis
elliptic paraboloid on z axis
hyperbolic paraboloid
ellipsoid
cone on y axis
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