Answer: The equation of an ellipse:
(
x
−
h
)
2
a
2
+
(
y
−
k
)
2
b
2
=
1
;
a
>
b
Has vertices at
(
h
±
a
,
k
)
Has foci at
(
h
±
√
a
2
−
b
2
,
k
)
Use the vertices to write 3 equations:
k
=
4
[1]
h
−
a
=
−
6
[2]
h
+
a
=
10
[3]
Use equations [2] and [3] to solve for h and a:
2
h
=
4
h
=
2
a
=
8
Use the focus to write another equation:
8
=
h
+
√
a
2
−
b
2
Substitute values for h and a:
8
=
2
+
√
8
2
−
b
2
6
=
√
64
−
b
2
36
=
64
−
b
2
b
2
=
64
−
36
b
2
=
28
b
=
√
28
Substitute the values into the standard form:
(
x
−
2
)
2
8
2
+
(
y
−
4
)
2
(
√
28
)
2
=
1