Assignment. Algebra 2. Name ID: 1

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1 Algebra Assignment Name ID: 1 Date Period Classif each conic section, write its equation in standard form, and sketch its graph. For parabolas, identif the verte and focus. For ellipses and hperbolas identif the vertices and foci. 1) = 0 Classif each conic section, write its equation in standard form, and sketch its graph. For circles, identif the center and radius. For ellipses and hperbolas identif the center. ) = 0 B ON0A1tl tkiuhtkaq _SnofstKwwaurNeo ZLHLYCk.h B ua\lxlc XrYiNgChAtCsJ iroems]earuvzewdu.^ `MraSdveu WwpimtIhR iijnsfhiwnniqtoek LAMlDgeLbkrzaE bw. -1- Worksheet b Kuta Software LLC

2 Classif each conic section, write its equation in standard form, and sketch its graph. For parabolas, identif the verte, focus, and eccentricit. For circles, identif the center and eccentricit. For ellipses and hperbolas identif the center, vertices, foci, and eccentricit. 3) = 0 ) = 0 Classif each conic section and sketch its graph. For parabolas, identif the verte and focus. For ellipses and hperbolas identif the vertices and foci. 5) = ( + 1) q J0C1cw hkfuitmah ssao`fxtrwtabrfeq QLtLZC].H g HAFlHlq qrlisgjhwtfsq bree]sfekrrvbezda.b _ jmua^dkel [wpistdhk \IDnPfWiUnjitseQ RAlgTebtrGau hy. -- Worksheet b Kuta Software LLC

3 Classif each conic section and sketch its graph. For circles, identif the center and radius. For ellipses and hperbolas identif the center. ) ( + 3) + ( + 1) = Classif each conic section and sketch its graph. For parabolas, identif the verte, focus, and eccentricit. For circles, identif the center and eccentricit. For ellipses and hperbolas identif the center, vertices, foci, and eccentricit. 7) ( 3) 9 + ( + 3) = 1 d BU0A1bi WKmuqtEaz XSSoBfutQwkakr\eA clbltcf.p U ]Aalqlk brliwg\hztxsc RraeasVedrv[ecdm.V N DMwaMduee ewziwtdhk LIbnqfAivnYi_toeA SAulhgZeMb^rfaY md. -3- Worksheet b Kuta Software LLC

4 ) ( + 1) 1 ( + 1) = 1 Identif the verte, focus, ais of smmetr, and directri of each. Then sketch the graph. 9) = 0 10) = 0 Use the information provided to write the transformational form equation of each parabola ) Verte: (10, ), Focus: ( 10, 3 ) 1) Verte: (, ), Focus: ( 53 ), 13) Verte at origin, Directri: = 1 1) Verte at origin, Focus: ( 0, 1 ) 15) Focus: ( 17, ), Directri: = 15 w wj0s1ug pkau]tgai GSoUfitjwiaAr_eh plulace.u E LASlwlE jri^gdhztosk ErQeLsXehrWveudG.q \ _MZavd\ea bwiiqtnhl ditntfsiqntipteeb ca`lygkelb`rkab cs. -- Worksheet b Kuta Software LLC

5 Identif the center, vertices, foci, length of the major ais, length of the minor ais, and eccentricit of each. Then sketch the graph. 1) ( + ) 5 + ( 1) 1 = 1 17) = 0 Use the information provided to write the standard form equation of each ellipse. 1) Vertices: ( 5, 1), ( 5, 9) Foci: ( 5, 1), ( 5, 7) 19) Foci: (, 0), (, 10) Endpoints of major ais: (, ), (, 1) a Z]0H1Kg GKbuMtKaH zscocfntnweaprpek qlpldct.e ` aaolzlf Yr\iggIhVtnss oreesiefrlveejdb.s k bmpajdte^ pwtiotwhv TIHnHfLiBnnijtke[ vaglmgcefbgrcaj Bz. -5- Worksheet b Kuta Software LLC

6 0) Identif the vertices, foci, asmptotes, and eccentricit of each. Then sketch the graph. 1) ( + ) 9 5 = 1 O pf0p1js YKYuGtAai usolfbthw^air_es MLuLqCI.F \ majlflo nrwi^g`hjtvsz FrOersjeXr_vBed\.m j JMaaGdkes HwZi]tmhM kijngfzianciwtjeg AAGlCgWeRbardaC Ra. -- Worksheet b Kuta Software LLC

7 Answers to Assignment (ID: 1) 1) Parabola = ( + 5) + Verte: (, 5) Focus: ( 9, 5 ) ) Circle ( + ) + ( + ) = Center: (, ) Radius: 3) 5) Ellipse ( + 1) ( + 1) + = 1 5 Center: ( 1, 1) Vertices: ( 1, ), ( 1, ) Foci: ( 1, 1 + 1), ( 1, 1 1) 1 Eccentricit: Parabola Verte: (, 1) Focus: ( 7, 1 ) ) ) Hperbola ( ) 1 = 1 Center: (, 0) Vertices: (5, 0), (3, 0) Foci: ( + 17, 0), ( 17, 0) Eccentricit: Circle Center: ( 3, 1) Radius: 7) 9) Ellipse Center: (3, 3) Vertices: (, 3), (0, 3) Foci: (3 +, 3), (3, 3) Eccentricit: Verte: (, 0) Directri: = 1 Focus: (, 1 ) Ais of Sm.: = 11) 1 ( ) = ( 10) 1) 1) = 15) 1 ( ) = ( ) ) 10) Hperbola Center: ( 1, 1) Vertices: (3, 1), ( 5, 1) Foci: ( 1 + 5, 1), ( 1 5, 1) 5 Eccentricit: 1.11 Verte: ( 3, 1) Directri: = ( + ) = ( + ) 13) 1 = Focus: ( 3, 1 ) Ais of Sm.: = 1 j M`0s1tg JKcuGtaT wsroufatjwvar]ez ulyldcq.e X VAzlhlS frviggwhdtgss krseoszezrbvoeed[.f W MuaFd_ew iwuiithhk livnvfjivnui[tef `AtllgLeobUrraC nf. -7- Worksheet b Kuta Software LLC

8 1) Center: (, 1) Vertices: (3, 1) ( 7, 1) Foci: (1, 1) ( 5, 1) Major Ais: 10 units Minor Ais: units Eccentricit: 3 5 = 0. 1) ( + 5) 1) 1 + ( + ) 5 = 1 19) ( + ) Vertices: (1, 0) ( 5, 0) Foci: ( + 3, 0) ( 3, 0) Asm.: = Eccentricit: = ) + ( + 5) 19 Center: (0, 3) Minor Ais: units Eccentricit: = 1 0) ( + ) Vertices: (7, 3) ( 7, 3) Foci: ( 3, 3) ( 3, 3) Major Ais: 1 units + ( + 1) 5 = 1 f pf0l1z] RKWuQtPa \SJogfmt[wwaBr\eP ZL^LKCd.M u ba`l[lu erki_gnhxtcse srsesweqrwvuekdo.w l smvatd^e\ kw[ihtbhk vitncfiivnliktyeq WAOlPgeYbraaS ub. -- Worksheet b Kuta Software LLC

You may recall from previous work with solving quadratic functions, the discriminant is the value

You may recall from previous work with solving quadratic functions, the discriminant is the value 8.0 Introduction to Conic Sections PreCalculus INTRODUCTION TO CONIC SECTIONS Lesson Targets for Intro: 1. Know and be able to eplain the definition of a conic section.. Identif the general form of a quadratic