Kuta Precalculus Circles/Ellipses Worksheet PDF

Acc. Precalculus - Unit 2 - Conics Name___________________________________ ©E K2E0e1`8y qKLuStpao RS_oqfXtCwjaVrCes ]LqLMCa.z y tAAlnlb nrjikgehVtmsB yrxebsoefrBvaeEdO. Day 1 - Circles/Ellipses Worksheet...

Acc. Precalculus - Unit 2 - Conics Name___________________________________ ©E K2E0e1`8y qKLuStpao RS_oqfXtCwjaVrCes ]LqLMCa.z y tAAlnlb nrjikgehVtmsB yrxebsoefrBvaeEdO. Day 1 - Circles/Ellipses Worksheet Date______________________ Period________ Use the information provided to write the standard form equation of each circle. 1) Center: (10, -5) 2) Center: (11, 7) Radius: 5 Radius: 38 (x-10)^2+(y-5)^2=25 (x-11)^2+(y-7)^2=38 3) Center: (10, 0) 4) Center: (-7, 3) Radius: 8 Radius: 6 2 (x-10)^2+y^2=64 (x+7)^2+(y-3)^2=72 5) Center: (14, -12) 6) Center: (-14, 1) Point on Circle: (18, -14) Point on Circle: (-13, 1) (x-14)^2+(y+12)^2=20 (x+14)^2+(y-1)^2=1 7) Ends of a diameter: (4, 8) and (-8, 14) 8) Ends of a diameter: (9, 18) and (11, 0) (x+2)^2+(y-11)^2=45 (x-10)^2+(y-9)^2=82 Identify the CENTER, VERTICES, CO-VERTICES, FOCI, LENGTH OF MAJOR AND MINOR AXIS and the ECCENTRICITY of each. ( x - 2) 2 ( y + 10) 2 ( x - 2) 2 ( y - 7) 2 9) + =1 10) + =1 49 64 81 49 center: (2,-10) center: (2,7) Vertices: (2,-2),(2,-18) vertices: (11,7),(-7,7) Co-Vertices: (9,-10),(-5,-10) co-vertices: (2,14),(2,0) Foci: (2,-10 + 15),(2,-10- 15 foci: 2+4 2, 7) , (2 - 4 2, 7) major axis: 16 units major axis: 18 units minor axis: 14 units minor axis: 14 units eccentricity: 15/8 eccetrinicity: 4 2/9 Worksheet by Kuta Software LLC -1- ©r r2O0n1C8V oKRu\tKaw tSVoPfot_wQaQrFe^ GL_LoCi.z C iAil[l[ HrsiLgWhjtksr HrweasbekrHvHe`dy.[ c hMSazdXej WwOiLtUhL ^IMnIfUiAnvittreh fPdrZeAcWaclCc\u\lEujsD.  2 11) ( ) x+ 17 2 + ( y + 10) 2 =1 center: (-17/2,-10) vertices: (7/2,-10),(-41/2, -10) 144 81 co-vertices: (-17/2,-1),(-17/2,-19) foci:(6 sqrt 7 -17/2,-10) major axis: 24 units minor axis: 18 units eccentricity: sqrt 7/4 Plot the CENTER and RADIUS of each. Then sketch the graph. 2 2 2 2 12) ( x - 4) + ( y - 1) = 5 13) x + ( y - 3) = 9 y y 8 8 6 6 4 4 2 2 -8 -6 -4 -2 2 4 6 8 x -8 -6 -4 -2 2 4 6 8 x -2 -2 -4 -4 -6 -6 -8 -8 2 2 2 2 14) x + y = 30 15) x + ( y + 2) = 4 y y 8 8 6 6 4 4 2 2 -8 -6 -4 -2 2 4 6 8 x -8 -6 -4 -2 2 4 6 8 x -2 -2 -4 -4 -6 -6 -8 -8 Worksheet by Kuta Software LLC -2- ©h K2t0p1q8z WKFuptmaU ySxoqfMtowHaCrNe[ CLyLKCs.[ g zAvlGls jrOisgehxtysF frueJsIeDrVvWeFdu.O l JMwaudneD rwfiBt]hF JIOnVfai^noiJtBeN UPlrQencxaklVccuhlAuxsb.  Sketch the graph. Plot the CENTER, FOCI, VERTICES and CO-VERTICES. ( x - 2) 2 y 2 ( x - 1) 2 ( y + 2) 2 16) + =1 17) + =1 4 49 36 9 y y 8 8 6 6 4 4 2 2 -8 -6 -4 -2 2 4 6 8 x -8 -6 -4 -2 2 4 6 8 x -2 -2 -4 -4 -6 -6 -8 -8 2 2 x ( y + 2) 18) + =1 30 10 y 8 6 4 2 -8 -6 -4 -2 2 4 6 8 x -2 -4 -6 -8 Worksheet by Kuta Software LLC -3- ©Z r2q0x1W8R pKWuxtlaA LSxoGfwtmwJaRr^ei yLlLUCC.e ] vAWlylc rrIiMgihYtOsg krMe^sTe`rqvweCdh.J L fM`a]dNef GwHiGtVhw \IsnIfhiNnTiYthew cPkrWeTc`aAlecauvlEu\sZ.  2 ( y - 4) 2 19) ( x - 2) + =1 9 y 8 6 4 2 -8 -6 -4 -2 2 4 6 8 x -2 -4 -6 -8 Worksheet by Kuta Software LLC -4- ©i j2f0p1Y8k mKpu_tdaI ESEoafMtbweahrYew ZLULSCR.O t SAYlYlT trjiYgxhxttsh Urre`sLesrjvSecdT.E Z uMgaydYeF rw_iMtghJ ZIKn`fpiWnxixtReU TPKrMeWcSaUltckuElzuQsO.  Answers to Day 1 - Circles/Ellipses Worksheet 1) ( x - 10) 2 + ( y + 5) 2 = 25 2) ( x - 11) + ( y - 7) = 38 2 2 3) ( x - 10) + y = 64 2 2 4) ( x + 7) 2 + ( y - 3) 2 = 72 2 2 5) ( x - 14) + ( y + 12) = 20 2 2 6) ( x + 14) + ( y - 1) = 1 7) ( x + 2) 2 + ( y - 11) 2 = 45 2 2 8) ( x - 10) + ( y - 9) = 82 9) Center: (2, -10) 10) Center: (2, 7) Vertices: (2, -2), (2, -18) Vertices: (11, 7), (-7, 7) Co-vertices: (9, -10), (-5, -10) Co-vertices: (2, 14), (2, 0) Foci: (2, -10 + 15 ), (2, -10 - 15 ) Foci: (2 + 4 2, 7), (2 - 4 2, 7) Major Axis: 16 units Major Axis: 18 units Minor Axis: 14 units Minor Axis: 14 units 15 4 2 Eccentricity: » 0.484 Eccentricity: » 0.629 8 9 17 11) Center: - , -10 2 ( ) 12) 8 6 y Center: (4, 1) Radius: 5 7 ( )( ) Vertices: , -10 , - , -10 2 41 2 4 2 17 ( )( ) Co-vertices: - , -1 , - , -19 2 17 2 -8 -6 -4 -2 -2 -4 2 4 6 8 x Foci: ( 6 7 - 17 2 , -10 , -6 7 - 17 2 )( , -10 ) -6 -8 Major Axis: 24 units Minor Axis: 18 units 7 Eccentricity: » 0.661 4 13) y 14) y 8 Center: (0, 3) 8 Center: (0, 0) Radius: 3 Radius: 30 6 6 4 4 2 2 -8 -6 -4 -2 2 4 6 8 x -8 -6 -4 -2 2 4 6 8 x -2 -2 -4 -4 -6 -6 -8 -8 15) y 16) y 8 Center: (0, -2) 8 Center: (2, 0) Radius: 2 Vertices: (2, 7) 6 6 (2, -7) 4 4 Co-vertices: (4, 0) 2 2 (0, 0) Foci: (2, 3 5 ) -8 -6 -4 -2 2 4 6 8 x -8 -6 -4 -2 2 4 6 8 x (2, -3 5 ) -2 -2 -4 -4 -6 -6 -8 -8 Worksheet by Kuta Software LLC -5- ©L P2N0y1m8c TKGuDtEaF ZSxoOfBtYwxaxrceJ MLrLhC^.E V `Aqlglb prhiDgJhZt_sm pr_eMsieGrIvGeMdH.S \ [M`azdVeG ZwqiStihE rIJnpfSiznZiPtNe_ VPhrVejcxatlecuuAlzufs]. 17) y 18) y 8 Center: (1, -2) 8 Center: (0, -2) Vertices: (7, -2) Vertices: ( 30, -2) 6 (-5, -2) 6 (- 30, -2) 4 Co-vertices: (1, 1) 4 Co-vertices: (0, -2 + 10 ) 2 (1, -5) 2 (0, -2 - 10 ) Foci: (1 + 3 3, -2) Foci: (2 5, -2) -8 -6 -4 -2 2 4 6 8 x (1 - 3 3, -2) -8 -6 -4 -2 2 4 6 8 x (-2 5, -2) -2 -2 -4 -4 -6 -6 -8 -8 19) y 8 Center: (2, 4) Vertices: (2, 7) 6 (2, 1) 4 Co-vertices: (3, 4) 2 (1, 4) Foci: (2, 4 + 2 2 ) -8 -6 -4 -2 2 4 6 8 x (2, 4 - 2 2 ) -2 -4 -6 -8 Worksheet by Kuta Software LLC -6- ©G G2B0m1S8r \KTuBtsaY yS_ohfIt`waawrZen hLDLhCB.c W pAKlAl` CrJiwgYhBtRsF qrRe^sneQrlvPeCdp.c q HMAaEdjeL xwuiCtQhn GIrnjfeiUnai\tueU NPJrjevcYasl[cfuNl`uHsF.