Graphing and Properties of Ellipses - Kuta Software

-1-
©N R21091i1c nK4uftfaj 1Sco9fktKwWaKr4eL TLULzCH.B J tAilklD frnitgQhrtAsU nrnehsSegr 2v1eddT.t 4 JMoaDdVeb owaijtzha lIAnjfYi7np itCeS TA1lYgIenbprbaD s2w.1 Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Graphing and Properties of Ellipses
Date________________ Period____
Identify the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis of each.
1) x2
49 + y2
x2
= 1 2)
169 36 + y2
16 = 1
3) x2
95 + y2
30 = 1 4) x 2
169 + y2
64 = 1
5) x2
64
+
(y − 6)2
121
= 1 6)
(x + 5)2
81
+
(y − 1)2
144
= 1

-2-
©5 g2G0L181P JKBuVtla7 SSKoRfPtAw7aYrLee LLtLGC4.J m OAZlFla drq igIhttYss prReMsOevr HvCevdJ.s K dMOagdMeq Owsiwt1hG 1IcnafDisnaiUt4ea 6AVlggreRb0rpaD b2n.2 Worksheet by Kuta Software LLC
7)
(x − 3)2
49
(y − 9)2
+ = 1 8) x2
4
64
+
(y − 8)2
9
= 1
Graph each equation.
9) x2
4 + y2
9 = 1 x
10) x2
49 + y2 = 1
8
y
8
y
6
4
2
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x

-3-
©W U2x0z1r1R fK3uxtrai DSGoUfbtZwva8rpeY yLKLSCA.q 9 SA4lwlm ArIi5glhutksj Arue1sFecr7vVeQd7.7 u GMZaxdnek xw2iKtlha uIRnLftilnRigt2e7 XAblAgle8b9rsaz F2k.V Worksheet by Kuta Software LLC
11) x2
36 + y2
8
y
12) x2
9 + y2
8
y
25 = 1 x
49 = 1 x
6
4
2
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
13) x2
49
+
(y − 3)2
16
= 1
14)
(x − 1)2
4
+ y2
49 = 1 x
8
y
8
y
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8

-4-
©U 32o0B1H1F XK8u7thaQ ESDo6f9tlwfacrSej HLjLLCw.2 s pA9lClh mrpiVgIh8t9sw BrNeFsieNr5vFehdW.g P oMzaYdIea BwZi1tHhH rIWnhfcionGirtEeY 3AjlRguejbGr6am y2D.X Worksheet by Kuta Software LLC
15) x2
49
+
(y − 1)2
9
8
y
= 1
16) (x + 5) 2 + y2
8
y
49 = 1 x
6
4
2
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
Identify the length of the major axis, length of the minor axis, length of the latus rectum, and eccentricity of
each.
17) −16y + 52 = −2x 2 − 8x − y 2 18) 4y 2 − 338x + 32y = −169x 2 + 443
19)
(x + 4)2
4
(y + 9)2
+
64
= 1
20) 126y + 9y 2 − 8x − 131 = −4x 2

-1-
©y M2O0w1a1w eKVuItOao fSLogfStFwjaor Ked 2L2LACY.0 f jABl0 l 4r7iIg5hwtEsB orheMsyezrHvye2dQ.U O fMCaydmey 4wBiot8hc gIRnXfUicngiot8er NABl6gRe3bvr taC O2Z.9 Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Graphing and Properties of Ellipses
Date________________ Period____
Identify the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis of each.
1) x2
49 + y2
169 = 1
Center: (0, 0)
Vertices: (0, 13), (0, −13)
Co-vertices: (7, 0), (−7, 0)
Foci: (0, 2 30), (0, −2 30)
Major Axis: 26 units
Minor Axis: 14 units
2) x2
36 + y2
16 = 1
Center: (0, 0)
Vertices: (6, 0), (−6, 0)
Co-vertices: (0, 4), (0, −4)
Foci: (2 5, 0), (−2 5, 0)
Major Axis: 12 units
Minor Axis: 8 units
3) x2
95 + y2
30 = 1
Center: (0, 0)
Vertices: ( 95, 0), (− 95, 0)
Co-vertices: (0, 30), (0, − 30)
Foci: ( 65, 0), (− 65, 0)
Major Axis: 2 95 units
Minor Axis: 2 30 units
4)
x 2
169 + y2
64 = 1
Center: (0, 0)
Vertices: (13, 0), (−13, 0)
Co-vertices: (0, 8), (0, −8)
Foci: ( 105, 0), (− 105, 0)
Major Axis: 26 units
Minor Axis: 16 units
5) x2
64
+
(y − 6)2
121
= 1
Center: (0, 6)
Vertices: (0, 17), (0, −5)
Co-vertices: (8, 6), (−8, 6)
Foci: (0, 6 + 57), (0, 6 − 57)
Major Axis: 22 units
Minor Axis: 16 units
6)
(x + 5)2
81
(y − 1)2
+ = 1
144
Center: (−5, 1)
Vertices: (−5, 13), (−5, −11)
Co-vertices: (4, 1), (−14, 1)
Foci: (−5, 1 + 3 7), (−5, 1 − 3 7)
Major Axis: 24 units
Minor Axis: 18 units

-2-
©2 J2c02121H NKQuNtra3 RSWoCfHtnwMaCrWek 0LnLWCi.g 1 lAMlxlK orqiagjh0tksP YrGepsLeQr HvuejdH.P z lMlaBd5ew WwziRt0hP dIKnqfiiDnGiVtTeM aA0l6g9eYborHaS i2f.4 Worksheet by Kuta Software LLC
7)
(x − 3)2
49
(y − 9)2
+ = 1
4
Center: (3, 9)
Vertices: (10, 9), (−4, 9)
Co-vertices: (3, 11), (3, 7)
Foci: (3 + 3 5, 9), (3 − 3 5, 9)
Major Axis: 14 units
Minor Axis: 4 units
8) x2
64
+
(y − 8)2
9
= 1
Center: (0, 8)
Vertices: (8, 8), (−8, 8)
Co-vertices: (0, 11), (0, 5)
Foci: ( 55, 8), (− 55, 8)
Major Axis: 16 units
Minor Axis: 6 units
Graph each equation.
9) x2
4 + y2
9 = 1 x
10) x2
49 + y2 = 1
8
y
8
y
6
4
2
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x

-3-
©1 a2z0s1W1S PKHuYtVaJ zSyo4fAtwwaadrAed vLJL6C5.e 6 bAvlclz 5rpiYgAhotlsR Dr9ewsJeprRvaebd5.S C uM2aFdQev fwzi6txh5 oIan6fAi6nWiytZeo PA4lPgJeTbYruat s2F.3 Worksheet by Kuta Software LLC
11) x2
36 + y2
8
y
12) x2
9 + y2
8
y
25 = 1 x
49 = 1 x
6
4
2
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
13) x2
49
+
(y − 3)2
16
= 1
14)
(x − 1)2
4
+ y2
49 = 1 x
8
y
8
y
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8

-4-
©x U2L0s1S1O UKXuntXaJ YStoZfntFw3aBrDei nLBL7Cr.I t qABlolF ZrgihgUh7t2sC vraeBsVeDr8v5ezd6.D z BMqaGdden JwSi1tIhY UIXnBfViUn3igtcel 9AwlbgyeqbwrGa2 22x.B Worksheet by Kuta Software LLC
15) x2
49
+
(y − 1)2
9
8
y
= 1
16) (x + 5) 2 + y2
8
y
49 = 1 x
6
4
2
6
4
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
Identify the length of the major axis, length of the minor axis, length of the latus rectum, and eccentricity of
each.
17) −16y + 52 = −2x 2 − 8x − y 2
Latus Rectum: 2 5 units
Latus Rectum: 8
2
13 units
Eccentricity:
2 ≈ 0.707 165
Eccentricity: ≈ 0.988
13
18) 4y 2 − 338x + 32y = −169x 2 + 443
Major Axis: 4 5 units
Major Axis: 26 units
Minor Axis: 2 10 units
Minor Axis: 4 units
19)
(x + 4)2
4
(y + 9)2
+ = 1
64
Major Axis: 16 units
Minor Axis: 4 units
Latus Rectum: 1 unit
15
Eccentricity: ≈ 0.968
4
20) 126y + 9y 2 − 8x − 131 = −4x 2
Major Axis: 24 units
Minor Axis: 16 units
Latus Rectum: 32
3 units
Eccentricity:
5
3 ≈ 0.745
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com