3
(
y
−
2
)
2
−
12
Substitute
3
(
y
−
2
)
2
−
12
for
3
y
2
−
12
y
in the equation
x
2
+
3
y
2
−
12
y
=
−
9
.
x
2
+
3
(
y
−
2
)
2
−
12
=
−
9
Move
−
12
to the right side of the equation by adding
12
to both sides.
x
2
+
3
(
y
−
2
)
2
=
−
9
+
12
Add
−
9
and
12
.
x
2
+
3
(
y
−
2
)
2
=
3
Divide each term by
3
to make the right side equal to one.
x
2
3
+
3
(
y
−
2
)
2
3
=
3
3
Simplify each term in the equation in order to set the right side equal to
1
. The standard form of an ellipse or hyperbola requires the right side of the equation be
1
.
x
2
3
+
(
y
−
2
)
2
=
1
