PreCalculus
Ellipse Questions
Use the information provided to write the standard form equation of each ellipse,
1) 9x2+4y2+72x-Sy-176=O
2) 16x2 + y2-64x+4y+4=O
3) Vertices: (-6, 4), (-6,-24)
Co-vertices: (4,-10), (-16,-10)
4) Vertices: (7, 20), (7,-4)
Co-vertices: (15, 8), (-1, 8)
5) Vertices: (-10, 5), (-10,-5)
Foci: (-10, 4), (-10,-4)
6) Vertices: (-6, 12), (-6,-14)
Foci: (-6, 11), (-6,-13)
7) Foci: (-7, 4), (-7,-6)
Co-vertices: (5,-1), (-19,-1)
8) Foci: (-3, 4), (-3,-6)
Co-vertices: (9, -1), (-15, -1)
9) Foci: (-3, 1), (-3,-5)
Endpoints of major axis: (-3, 3), (-3,-7)
10) Foci: (0, 2), (0,-6)
Endpoints of major axis: (0, 3), (0,-7)
11) Foci: (-1, -5), (-1, -15)
Endpoints of minor axis: (11,-10), (-13,-10)
12) Foci: (-4, 2), (-4,-22)
Endpoints of minor axis: (1,-10), (-9, -1 O)
14) Center: (-2, 1 O)
Vertex: (-2, 5)
Focus: (-2, 6)
13) Center: (3, 10)
Vertex: (3, -3)
Focus: (3, 5)
15) Center: (2, 10)
Focus: (2, 14)
Co-vertex: (5, 1 O)
16) Center: (6, 10)
Focus’ (18, 10)
Co-vertex: (6, 5)
17) Endpoints of major axis: (16, 10), (-8, 10)
Endpoints of minor axis: (4, 20), (4, 0)
18) Endpoints of major axis: (-4, 4), (-14, 4)
Endpoints of minor axis: (-9, 8), (-9, 0)
19) Major axis is horizontal
Center: (-5,-8)
Major axis is 20 units long
Minor axis is 2 units long
20) Major axis is horizontal
Center: (-5, 7)
Major axis is 16 units long
Minor axis is 6 units long
21)
22)
y
’5 -4 -2
5
23) Eccentricity’ 13
Foci: (-1, 0), (-11, 0)
3
24) Eccentricity=5
Foci: (13,-1), (7,-1)
4
25) Eccentricity=5
Center: (-7,-1)
Vertex: (-12,-1)
26) Eccentricity-
12
13
Center: (-4,-1)
Vertex: (-17,-1)
Identify the center, vertices, co-vertices, foci, and eccentricity of each. Then sketch the graph.
27) (x + 1)2+ y2
=1
16
28)
y
-3-
+
36
16
-1
Answers to Ellipse Questions
1)
4)
7)
(X+4)2 (y--l)2
36
+
81
(X- 7)2 (y- 8)2
64
+
144
(X + 7)2 (y + 1)2
144
+
169
2)
-1
5) (X+10)2 y2
=1
8)
9
10) --+
9
13)
(x-3)
-1
25
+
(y- lo)
=1
(X+3)2 (y+ 1)2
14)
144
169
(X-6)2 (y- 10)2
+
16)
=1
169
25
17)
19) (x + 5)2 + (y q- 8)2= 1
20)
100
2
X (y-4)2
(x + 6)2
22) --+
-1
23)
36 9
169
(x + 7)2 (y + 1)2
25)
+
-1
26)
25 9
27)
Y
3)
6)
+---1
25
+
144
169
(x + 1)2 (y + 10)2
+
11)
=1
144
169
2
X (y + 2)2
(X- 2)2 (y + 2)2
+ -1
4 64
-1
(x + 6)2
25
9)
-1
12)
(x + 4)2
25
(x + 6)2
100
+
+
(y + 10)2
=1
196
(y+ 1)2
-1
169
(y + 2)2
-1
16
25
(y+ 10)2
=1
169
(X- 2)2
(y - 10)2
+
=1
9
25
(X+ 9)2
(y-4)2
+
-1
25
16
(X + 3)2
+
(y - 10)2
=1
15)
9
25
(x-4)2
(y-10)2.
+
=1
18)
144
100
2
2
(x + 5)2 (y- 7)2
X
+
-1
+ Y-~-- 1
21)
64
9
49 36
2
2
y
(x - 10)
(y + 1)2
+
-1
24)
+
=1
144
25
16
(X + 4)2
(y+ 1)2
+
-1
169
25
28)
(X + 2)2
+
~y
Center: (-1, 0)
Vertices: (3, 0)
(-5, o)
(-1, -i)
Center: (21--, -1)
Vertices: (~,-1)
Co-vertices: (-1, 1)
(--~-,-1)
1
>.Foci: (-1 + "Q~-, O)
X (-1 - "~i7-, 0)
Eccentricity: --~ ~ 0.968
Eccentricity: -~-- ~ 0.745
-4-