Graphing and Properties of Ellipses - Kuta Software
Graphing and Properties of Ellipses - Kuta Software
Graphing and Properties of Ellipses - Kuta Software
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-1-<br />
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<strong>Kuta</strong> S<strong>of</strong>tware - Infinite Algebra 2<br />
Name___________________________________<br />
<strong>Graphing</strong> <strong>and</strong> <strong>Properties</strong> <strong>of</strong> <strong>Ellipses</strong><br />
Date________________ Period____<br />
Identify the center, vertices, co-vertices, foci, length <strong>of</strong> the major axis, <strong>and</strong> length <strong>of</strong> the minor axis <strong>of</strong> each.<br />
1) x2<br />
49 + y2<br />
x2<br />
= 1 2)<br />
169 36 + y2<br />
16 = 1<br />
3) x2<br />
95 + y2<br />
30 = 1 4) x 2<br />
169 + y2<br />
64 = 1<br />
5) x2<br />
64<br />
+<br />
(y − 6)2<br />
121<br />
= 1 6)<br />
(x + 5)2<br />
81<br />
+<br />
(y − 1)2<br />
144<br />
= 1
-2-<br />
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7)<br />
(x − 3)2<br />
49<br />
(y − 9)2<br />
+ = 1 8) x2<br />
4<br />
64<br />
+<br />
(y − 8)2<br />
9<br />
= 1<br />
Graph each equation.<br />
9) x2<br />
4 + y2<br />
9 = 1 x<br />
10) x2<br />
49 + y2 = 1<br />
8<br />
y<br />
8<br />
y<br />
6<br />
4<br />
2<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
x
-3-<br />
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11) x2<br />
36 + y2<br />
8<br />
y<br />
12) x2<br />
9 + y2<br />
8<br />
y<br />
25 = 1 x<br />
49 = 1 x<br />
6<br />
4<br />
2<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
13) x2<br />
49<br />
+<br />
(y − 3)2<br />
16<br />
= 1<br />
14)<br />
(x − 1)2<br />
4<br />
+ y2<br />
49 = 1 x<br />
8<br />
y<br />
8<br />
y<br />
6<br />
6<br />
4<br />
4<br />
2<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
x<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8
-4-<br />
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15) x2<br />
49<br />
+<br />
(y − 1)2<br />
9<br />
8<br />
y<br />
= 1<br />
16) (x + 5) 2 + y2<br />
8<br />
y<br />
49 = 1 x<br />
6<br />
4<br />
2<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
x<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
Identify the length <strong>of</strong> the major axis, length <strong>of</strong> the minor axis, length <strong>of</strong> the latus rectum, <strong>and</strong> eccentricity <strong>of</strong><br />
each.<br />
17) −16y + 52 = −2x 2 − 8x − y 2 18) 4y 2 − 338x + 32y = −169x 2 + 443<br />
19)<br />
(x + 4)2<br />
4<br />
(y + 9)2<br />
+<br />
64<br />
= 1<br />
20) 126y + 9y 2 − 8x − 131 = −4x 2
-1-<br />
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<strong>Kuta</strong> S<strong>of</strong>tware - Infinite Algebra 2<br />
Name___________________________________<br />
<strong>Graphing</strong> <strong>and</strong> <strong>Properties</strong> <strong>of</strong> <strong>Ellipses</strong><br />
Date________________ Period____<br />
Identify the center, vertices, co-vertices, foci, length <strong>of</strong> the major axis, <strong>and</strong> length <strong>of</strong> the minor axis <strong>of</strong> each.<br />
1) x2<br />
49 + y2<br />
169 = 1<br />
Center: (0, 0)<br />
Vertices: (0, 13), (0, −13)<br />
Co-vertices: (7, 0), (−7, 0)<br />
Foci: (0, 2 30), (0, −2 30)<br />
Major Axis: 26 units<br />
Minor Axis: 14 units<br />
2) x2<br />
36 + y2<br />
16 = 1<br />
Center: (0, 0)<br />
Vertices: (6, 0), (−6, 0)<br />
Co-vertices: (0, 4), (0, −4)<br />
Foci: (2 5, 0), (−2 5, 0)<br />
Major Axis: 12 units<br />
Minor Axis: 8 units<br />
3) x2<br />
95 + y2<br />
30 = 1<br />
Center: (0, 0)<br />
Vertices: ( 95, 0), (− 95, 0)<br />
Co-vertices: (0, 30), (0, − 30)<br />
Foci: ( 65, 0), (− 65, 0)<br />
Major Axis: 2 95 units<br />
Minor Axis: 2 30 units<br />
4)<br />
x 2<br />
169 + y2<br />
64 = 1<br />
Center: (0, 0)<br />
Vertices: (13, 0), (−13, 0)<br />
Co-vertices: (0, 8), (0, −8)<br />
Foci: ( 105, 0), (− 105, 0)<br />
Major Axis: 26 units<br />
Minor Axis: 16 units<br />
5) x2<br />
64<br />
+<br />
(y − 6)2<br />
121<br />
= 1<br />
Center: (0, 6)<br />
Vertices: (0, 17), (0, −5)<br />
Co-vertices: (8, 6), (−8, 6)<br />
Foci: (0, 6 + 57), (0, 6 − 57)<br />
Major Axis: 22 units<br />
Minor Axis: 16 units<br />
6)<br />
(x + 5)2<br />
81<br />
(y − 1)2<br />
+ = 1<br />
144<br />
Center: (−5, 1)<br />
Vertices: (−5, 13), (−5, −11)<br />
Co-vertices: (4, 1), (−14, 1)<br />
Foci: (−5, 1 + 3 7), (−5, 1 − 3 7)<br />
Major Axis: 24 units<br />
Minor Axis: 18 units
-2-<br />
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7)<br />
(x − 3)2<br />
49<br />
(y − 9)2<br />
+ = 1<br />
4<br />
Center: (3, 9)<br />
Vertices: (10, 9), (−4, 9)<br />
Co-vertices: (3, 11), (3, 7)<br />
Foci: (3 + 3 5, 9), (3 − 3 5, 9)<br />
Major Axis: 14 units<br />
Minor Axis: 4 units<br />
8) x2<br />
64<br />
+<br />
(y − 8)2<br />
9<br />
= 1<br />
Center: (0, 8)<br />
Vertices: (8, 8), (−8, 8)<br />
Co-vertices: (0, 11), (0, 5)<br />
Foci: ( 55, 8), (− 55, 8)<br />
Major Axis: 16 units<br />
Minor Axis: 6 units<br />
Graph each equation.<br />
9) x2<br />
4 + y2<br />
9 = 1 x<br />
10) x2<br />
49 + y2 = 1<br />
8<br />
y<br />
8<br />
y<br />
6<br />
4<br />
2<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
x
-3-<br />
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11) x2<br />
36 + y2<br />
8<br />
y<br />
12) x2<br />
9 + y2<br />
8<br />
y<br />
25 = 1 x<br />
49 = 1 x<br />
6<br />
4<br />
2<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
13) x2<br />
49<br />
+<br />
(y − 3)2<br />
16<br />
= 1<br />
14)<br />
(x − 1)2<br />
4<br />
+ y2<br />
49 = 1 x<br />
8<br />
y<br />
8<br />
y<br />
6<br />
6<br />
4<br />
4<br />
2<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
x<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8
-4-<br />
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15) x2<br />
49<br />
+<br />
(y − 1)2<br />
9<br />
8<br />
y<br />
= 1<br />
16) (x + 5) 2 + y2<br />
8<br />
y<br />
49 = 1 x<br />
6<br />
4<br />
2<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
x<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
Identify the length <strong>of</strong> the major axis, length <strong>of</strong> the minor axis, length <strong>of</strong> the latus rectum, <strong>and</strong> eccentricity <strong>of</strong><br />
each.<br />
17) −16y + 52 = −2x 2 − 8x − y 2<br />
Latus Rectum: 2 5 units<br />
Latus Rectum: 8<br />
2<br />
13 units<br />
Eccentricity:<br />
2 ≈ 0.707 165<br />
Eccentricity: ≈ 0.988<br />
13<br />
18) 4y 2 − 338x + 32y = −169x 2 + 443<br />
Major Axis: 4 5 units<br />
Major Axis: 26 units<br />
Minor Axis: 2 10 units<br />
Minor Axis: 4 units<br />
19)<br />
(x + 4)2<br />
4<br />
(y + 9)2<br />
+ = 1<br />
64<br />
Major Axis: 16 units<br />
Minor Axis: 4 units<br />
Latus Rectum: 1 unit<br />
15<br />
Eccentricity: ≈ 0.968<br />
4<br />
20) 126y + 9y 2 − 8x − 131 = −4x 2<br />
Major Axis: 24 units<br />
Minor Axis: 16 units<br />
Latus Rectum: 32<br />
3 units<br />
Eccentricity:<br />
5<br />
3 ≈ 0.745<br />
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