I
6i6
Example
p'
Write each equation in standard form. State whether the graph of the equation
is
parabola, circle, ellipse, or hyperbora. Then graph the equ"ation.
l. x2++f-e*+76y-11:0
!. 9y2 - L6x2 - lgy - 64x - 799 = 0
Example
2
P.657
2.
x2+f+tZx-By+36:0
4.6y2-24y+28*x=0
Without writing in standard form, state whether the graph of each equation is
parabola, circle, ellipse, or hyperbola.
5.4x2+6f-3x-2y:!2
7.
8x2
9.
4x2
+
8f + L6x + 24:
a
a
6.5y2:2x*6y-8+3x2
8.4x2-6y=8x+2
O
- 3y, + 8xy - 12:2x -t U
ll. S* * 12xy * 76y2 + 4y - 3x: 12
10. Sxy
-
12. 76xy
3x2
+
+
6y2
+ tZy = tg
+ 8y2 -
8x2
7Bx
* 8y:19
15. AvlATloN A military jet performs for an air show. The path of the plane
during one maneuver can be modeled by a conic section with equition
24x-2 + L000y
- 37,680x - 4s,600: 0, where distances are represented
in feet.
a. Identify the shape of the curved path of the jet. write the equation in
standard form.
b. If the jet begins its path upward, or ascent, at x O,what is the horizontal distance
=
traveled by the jet from the beginning of the ascent to the end of the descent?
c. VVhat is the maximum height of the jet?
:
*
I
656
Example
P'
Write each equation in standard {orm. State whether the graph of the equation is
parabola, circle, ellipse, or hyperbora. Then graph the equition.
14.
+ 78x + By 16. x2 * y2:16 + 6y
18. 7x2 - 8y :84x - 2y2 3x2
20. 4y2
-
2y,
:24y
x
-
P-
2
6s7
35
:
15.
0
3x2
+ 24x +
776
21. 772y
-
4y2
-
+Oyt
52
=
0
17.32x*28:y-8x2
19. x2+8y:77*6x-y2
3L
22. 28x2 + 9y2 - 188 = S6x
Example
Step-by-Step Solutions begin on page R20.
Extra Practice begins on page947.
*
64x
=
25. 25x2 + 384y
36y
488
-
+
64y2
7y2
-
8x2
-t 2OOx:1776
Without writing in standard form, state whether the graph of each equation is
parabola, circle, ellipse, or hyperbola.
24,
4x2
-
5y
:9x -
12x: l\y - fuz
fiF rsr' - 76y :72x - 4y2 + 7e
29. Sxy * 12x2 - 16x:5y + 3y2 + 78
25. 4x2
12
26. 9x2 -t 12y :9y2 + t8y - tO
28. 12y2 - 4xy + 9x2: t8x - 124
30. 19x2 + 14y
12. 5x - 12xy
:6x -
I
6x2
=
19y2
Ay2
-
-
51.
88
Z+y
54. LIGHT A lamp standing near
-
a
O
-
8x2 4-
2Oxy*
18
:
15. 18x - 24y + 324xy
4y2
:
-
t2 + 9x
27x2
+
3y2
-
S
a wall throws an arc of light in the shape of a conic
section. Suppose the edge of the light can be represented by the equation
3y' - 2y - 4x2 + 2x - 8 = 0. Identify the shape of the edgeof the light and graph
the equation.
558
Chapter 10 Conic Sections
a