Name_~~4· Date, Algebra II Pre AP Conics Review Worksheet ~ _ Period __ Identify the conic and write each of the following in standard form. c c (1t- 2..) ~ -I- ~ ~.::. Olo S-r- = I~ (1[-1) ~ f. (,+ 3):a. (J{+ E I "J!2.. -'1 G (!1-z.) +- 1. X2 + y2 - 4x -16 2- :: I == I 4- + ( 'J ~L) 2. 2. X2 + y2 - 2x -/j (y -3) ~ ~:-i (~_ ¥) C!::J -I ) , =I -4 'K--: fJ f _ (1t+3);J.. /I I (jc-LJ:a. q- 4. X2+9y2 -36y+27 6. X2- 8x =0 =0 =0 + 2y + 16 = 0 7. X2_4y2 +Sy-S ~ 8. X2_9y2 +6x - (~~t) .,- =0 - =/ 2 9. 9x +4y2 -36x+Sy+4 I =0 10. 16x2 _9y2 -32x-54y-209 IfIJ 9 =0 2- (XJ-L):l._ (fJ 1-3)2.;: f/ 4X2 + y2 +24x-4y+36 !Jl..._1 9 e- 3. 2. ']C2.. tI + 10y + 10 = 0 5. y2 -4x-6y+9 1- =0 =0 Write each of the following in standard form then find all appropriate information. 11. 4X2 +9/ +Sx-36y+4 center (-I, =0 a..) -'-If z. J (2., 2..) endpts of minor axis (-(It)) ( - I:!: If5=- I endpts of latus rectum (- 2-, - foci 5", -if-) (~o) ( !»J .!:.J -8 J (S-:t..:l (S-, - L/ 1: ;J.. VZ equations of asymptotes 't -z:- -4) ) -? l.j ~ eccentricity VI()(-s) z!. """"i:"" y2+x+2y-8=O vertex ( ;!cf, ! J = (Cj l -I) focus ---=-+-- \{{OJ radius v:ll ~ :J 14. i=) =0 endpts of conjugate axis 2-) I x2+/+4x+9y-1=O center (-I, L/) (-/ ~ Vs 3 ( vertices (-I :f. v_ '~J '~) ~~4___ .e:«: V~ eccentricity 2X2 - y2 -20x-Sy+50 center endpts of major axis ( foci 13. 12. equation of directrix _-=-~,,---':. __ equation of axis of symmetry endpts of latus rectum si. c..( fj:. -I -3 ) (g 1./, 2: (H tt I -J.) Z. Using the following information, write an equation ( 1{.... "I"1)~ of-( 9-7) ~-::: i:J.S ~ 15. (X" 7 J.) 1.. +- 'J ~ := ( ~-'I) LI- (fj-4 t{ 8 L/ () (1(-3) .l:!I _---"y"-- J 18. Circle with center at .,lS-__________ 19. Ellipse foci (y-3J 20 + -;;-::I (1.j-4) 'z, (~-"iI --;-c - J at (6, 22) = 4 and tangent to both axes (6, 9) and tangent to the circle X2 + y2 + 4x - 6y -12 = 0 (3, (3, 2) and 11) and sum offocal radii is 16 20. Ellipse tangent to the x and y axis and the line x 20 () 1,3 and ( 9,3 = 10 with foci at ) l! - :. I 21. Vertical hyperbola with asymptotes y (jj-~)"). (~_.s-)l. I,. I __________ (x.,...l.) = 3x + 4 "2- ID_T-'---- __ ('t-s-)~ (1, 2) and (6, 12) Endpointsofdiameter 17. Circle with center in the first quadrant on the line x ZS'" of- (y- u.2. / (/ 2. Show all work. 16. Circle with center on the x axis and tangent to the line y )l..: ,(., (JC-G,)l.of-(~-ttl~ in standard form. = 2x + 3 and y = -2x + 5 and the difference of the focal radii is 8 == I 22. Hyperbola vertices at (5, 7) and (5, 9) and length of the conjugate axis is 8 {9-2.)'" l.. _-::_/~~~___ •._'1_-_.::._I_ 23. Hyperbola with center (-2, 2), a focus at (2, 2) and and length of the conjugate axis is 4 u= ",-..L ('K-{)~+.:ff J- 2. 24. parabola with directrix y 2.. 1C tz (':1 - .3 ) 1. - 2.. 25. parabola with directrix x = 3 and a focus = _2. at (1, 2) and a vertex at (-2, 3) 4 26. parabola where the directrix is the x-axis and the focus is (5, 1) ,'( 1t = 2:i q -I.{) -a. - ~ 27. parabola with the vertex at the center of the hyperbola 9x2 - 4 y2 + 90x + 8y + 185 = 0 and the focus at the center of the circle X2 + y2 - 4x - 2y - 20 = 0 28. circle whose diameter is the line segment joining the vertex and the focus of the parabola X2 -12y =0 ;;- .?"- Graph each of the following and indicate the domain and range. Y = 2.J1- X2 29. r ---P,"' ~ T .. I- t 1L =/ a, -l- (':1-1-) & -rr-r-r-r- I~ -1-, Tf'T'] r ! I I ! I I I I i I ! ! 4- !.... - -13 - - '" I I I ! ! , T 8 ! I I ·8 I -R t !, i I -~25+4y- ~ S ! 14 I 1 j ! r - I I•• :' -.S - - -5 -It - -12 -it 1 I II I I j 1 8 r I , I I " ,v vV'· y>2-~36-4(X-1)2 (!:J-J...) 1- ..:~'V !~ 34. jcl2.. CF .f-~_I v , I , 1 , j ! I I y2 +- (lj-2..)~= ~9 L I -r r I r 7 'L:. ec -4(x-I) 4(Y-I)~ +(lj-""L)'= (1c-O'Z. + (&-2.) -9 c;-r-r , I - i I I ! I j f l II' ! I I I , j 1 I rI - - ! I I I ! ',1 1/ i 1 I A•..• v 1/ ~'\ If 1/, -B -Q 3 ,1, -, J ! ! . '0\ f ! i I I I I 1 I I ! ! ( I , I I I 1 I I I i I i I i 1 I 8- ! I . I. I i I I r--P1+ f'..j , 1 . i 1 -~ 1 I I ! I I i I....-r ~ I I~ 1 , .v c/ - Dr"- . T 3 -B- I ! j I I , j ! T I I ! ~ 3' 2 =t .. r-t-r+-v-t- 'IL 1/1 Y I I••• 1/ I) t> 1...- I i 4- I ! I I r f i .1- f.--6 ~ rv I , 1 I, ~ 8- I 1 I~ , I r-n-& r r r ·5 I f-- +l- r 8 I J l,..; -l? -" ! I I I 1C.2. . .s 1 I ! I I I ! I j 32. X:::; 4 I r ! I ! , r ! I I I' ~ IF - 'J ;-(k: _3)1.+ 9 '2..:::. I-~ If j I i I I I , x>~1-y+3 ("-3): ~~U 2- 'K2- 31. - ~k..t SIu.J..- X=~9-(Y-2)2 30. ~AJ f...- 1/ 1/ - - -it ! i I I I i ' ! n- cP- , I 1 I I..•• L.- r'1 ," I I I ! . 7 8
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