Answer: The standard form for the equation of an ellipse is:
(
x
−
h
)
2
a
2
+
(
y
−
k
)
2
b
2
=
1
The center is:
(
h
,
k
)
The vertices on the major axis are:
(
h
−
a
,
k
)
and
(
h
+
a
,
k
)
The vertices on the minor axis are:
(
h
,
k
−
b
)
and
(
h
,
k
+
b
)
The foci are:
(
h
−
√
a
2
−
b
2
,
k
)
and
(
h
+
√
a
2
−
b
2
,
k
)
To put the given equation in standard form, change the + 2 to - -2 and write the denominators as squares:
(
x
−
3
)
2
4
2
+
(
y
−
−
2
)
2
3
2
=
1
The center is:
(
3
,
−
2
)
The vertices on the major axis are:
(
−
1
,
−
2
)
and
(
7
,
−
2
)
The vertices on the minor axis are:
(
3
,
−
5
)
and
(
3
,
1
)
Evaluate:
√
a
2
−
b
2
=
√
4
2
−
3
2
=
√
16
−
9
=
√
5
The foci are:
(
3
−
√
5
,
−
2
)
and
(
3
+
√
5
,
−
2
)
