If the divisor of
is larger than the divisor of
then the major axis is horizontal along
the
x
axis, as in Example 1. If the divisor of
is larger than the divisor of
then the major
axis is vertical along the
y
axis, as you will see in Example 2.
EXAMPLE 2
Graphing an Ellipse with a Vertical Major Axis
Graph the ellipse given by
Solution:
Write the equation in standard form by dividing by 16.
Since
this ellipse is elongated vertically.
and
Solve for
a
and
b.
and
Identify the vertices:
and (0,
a
).
and (0, 4)
Identify the
x
intercepts on the minor
axis:
and (
b
, 0).
and (1, 0)
Graph by labeling the points
(0, 4),
and (1, 0) and connecting
them with a smooth curve.
■
YOUR TURN
Graph the ellipses:
a.
b.
x
2
9
+
y
2
36
=
1
x
2
9
+
y
2
4
=
1
(

1, 0),
(0,

4),
(

1, 0)
(

b
, 0)
(0,

4)
(0,

a
)
b
=
1
a
=
4
b
2
=
1
a
2
=
16
16
7
1,
x
2
1
+
y
2
16
=
1
16
x
2
+
y
2
=
16.
x
2
,
y
2
y
2
,
x
2
(5, 0), (0,

3),
(

5, 0),
(0,

3)
(0,

b
)
(

5, 0)
(

a
, 0)
b
=
3
a
=
5
b
2
=
9
a
2
=
25
25
7
9,
x
2
25
+
y
2
9
=
1.
x
y
(0, 3)
(–5, 0)
(5, 0)
(0, –3)
Technology Tip
Use a graphing calculator to check
the graph of
Solve for
y
first. That is,
and
y
2
= 
3
A
1

x
2
25
.
y
1
=
3
A
1

x
2
25
x
2
25
+
y
2
9
=
1.
x
y
(0, 4)
(–1, 0)
(1, 0)
(0, –4)
■
Answer:
a.
b.
x
y
(0, 6)
(–3, 0)
(3, 0)
(0, –6)
x
2
9
y
2
36
+
= 1
x
y
(0, 2)
(–3, 0)
(3, 0)
(0, –2)
x
2
9
y
2
4
+
= 1
Study Tip
If the divisor of
is larger than the
divisor of
then the major axis is
horizontal along the
x
axis, as in
Example 1. If the divisor of
is
larger than the divisor of
then the
major axis is vertical along the
y
axis, as you will see in Example 2.
x
2
,
y
2
y
2
,
x
2
You've reached the end of your free preview.
Want to read all 10 pages?
 Summer '17
 juan alberto
 Vertex, MAJOR AXIS, Systems of Nonlinear Equations and Inequalities