11. x y 1; foci are ( 13, 0); vertices are ( 2, 0); asymptotes are y 3 2 x 12. x x 2. y 2 1; foci are ( 1, 0); vertices are ( 2, 0) 14.

Size: px

Start display at page:

Download "11. x y 1; foci are ( 13, 0); vertices are ( 2, 0); asymptotes are y 3 2 x 12. x x 2. y 2 1; foci are ( 1, 0); vertices are ( 2, 0) 14."

Camilla Flynn
5 years ago
Views:

1 66 Aitionl Answers. () I (, e ) lim 0 6. () I ( e,) lim 0 Section A.. ( ) (0, ) (0, ). The circle with center t (, 0) n rius plus its interior. 6. The region eterior to the unit circle n interior to the circle with center t (0, 0) n rius. 7. ; focus is (, 0); irectri is. ; focus is (, 0); irectri is 9. 6; focus is (0, /); irectri is /. ; focus is (0, /); irectri is /. ; foci re (, 0); vertices re (, 0); smptotes re. ; foci re (0, ); vertices re (0, ). ; foci re (, 0); vertices re (, 0). ; foci re (0, ); vertices re (0, ); smptotes re. Focus is (, 0); irectri is (0, 0) =. ( ) ( ) =. (0, ) (, ) 6. Focus is (0, /6); irectri is /6 (0, ). Center (, ); rius = 6 7. ; foci re (, 0) 6 F =. Center (, ); rius..

2 Aitionl Answers 67. ; foci re (0, ) 6. () Foci re ( 7, ); vertices re (0, ) n (, ); center is (, ). (, ) ; smptotes re ; foci re (, 0). ; smptotes re ; foci re (0, ) = () Verte is (, ); focus is (, ); irectri is = F.. F = = ( + ) = ( ) V = F 7. () Center is (, 0); foci re (, 0) n (7, 0); smptotes re ( ) ; vertices re (, 0) n (6, 0) ( ) = F V C ( ) 6 F V ( ) =. ( ) ( ); verte is (, ); focus is (, ); irectri is 9. ( ) ( ) ; vertices re (, ) n (, ); 6 9 foci re (, ); center is (, ) 0. ( ) ( ) ; vertices re (, ) n (0, ); foci re (, ) n (, ); center is (, ); smptotes re ( ). ( ) ( ) ; vertices re (, ) n (, 0); foci re (, ); center is (, ); smptotes re ( ). Circle; center is (, 0); rius is. Circle; center is (7, ); rius is. Prbol; focus is (, 0); verte is (, ). Ellipse; center is (, 0); foci re (, 0) n (0, 0); vertices re (, 0) 6. Hperbol; center is (, ); foci re (, ); vertices re (, ) n (0, ); smptotes re ( ) 7. Volume of the prbolic soli is V ph b ; volume of the cone is V p hb ; V V. () Volume of the soli forme b revolving A bout the -is is V p k ; volume of the soli forme b revolving B bout the -is is V V V p k ; V V : both equl to pk. 9. The slopes of the two tngents to p from the point (p, ) re p p m n m p, n m p m. 0. b ; re. () p 6p = 9

3 6 Aitionl Answers. p. p. w H. r A r B (r t A r B ) 0 r A r B constnt 6. PF will lws equl PB becuse the string hs constnt length AB FP PA AP PB. Section A.. e /; foci re (, 0); irectrices re /. e /; foci re (0, ); irectrices re. e /; foci re (0, ); irectrices re. e /; foci re (, 0); irectrices re e ; 9. e ; 6 c. Tke c n, then e n b. The eqution is. 9 c. Tke c n, then e n b. Therefore, is moel of Pluto s orbit. 6. ( ) ( ) ; foci re (, ); e ; irectrices re e /; foci re (, 0); irectrices re 6/ 6. e ; foci re (0, ); irectrices re 7. e ; foci re (, 0); irectrices re. e ; foci re (0, ); irectrices re / e ;. e ;. ( 6) ( ). 6 (e ). 0, b, c 0; e / Section A.. Hperbol. Prbol. Ellipse. Ellipse. Prbol 6. Hperbol 7. Prbol. Ellipse (circle) 9. Hperbol. Prbol. Hperbol. Hperbol. Ellipse. Hperbol. Ellipse 6. Prbol 7. () () ; hperbol. () () ; ellipse 9. () 60; prbol 0. () () ; ellipse. () ; prllel horizontl lines. () ; prllel horizontl lines. () 0; prbol. () () 0; hperbol. () () 9; ellipse 6. () () 7; hperbol 7. sin, cos ; or sin, cos. sin, cos ; or sin, cos 9. sin 0., cos 0.97; A 0., B 0.00, C., D 0.7, E.0, F; 0.().() ; ellipse 0. sin 0., cos 0.99; A.0, B 0.00, C.0, D.99, E 0.0, F7;.0().0() ; hperbol. sin 0., cos 0.9; A 0.00, B 0.00, C.00, D0, E0, F;.00() 0 or.00; prllel lines. sin 0., cos 0.9; A 0.00, B 0.00, C 0.00, D0, E0, F9; 0.00() 9 0; prllel lines. sin 0.6, cos 0.77; A.0, B 0.00, C 0.0, D.07, E 6.9, F;.0() 0.0() ; hperbol

4 Aitionl Answers 69. sin 0., cos 0.9; A 0., B 0.00, C., D., E 7.6, F6; 0.().() ; ellipse. () () () () () 6. Yes, the grph is hperbol: with AC 0 we hve AC 0 n B AC Yes, 0. BBcos 0 9. () Hperbol (c) At (, ): ; At (, ): [9., 9.] b [6., 6.] 0. () Flse. If A C, B, the grph is prbol. Flse. If A C, B, the grph is prbol. (c) True. B AC 0, the grph is hperbol.. () ( b ) ( ) ( ) ( ) b (c) () () () m (e) m m b. () ( ) ( ) b ( ) ( ) b (c) () () () m (e) mb. () Prbol The eqution cn be written in the form ( ) 0.. () Prbol The eqution cn be written in the form ( ) 0. Section A6. cosh ; tnh ; coth ; sech ; csch. cosh ; tnh ; coth ; sech ; csch. sinh ; tnh ; coth 7 ; sech ; csch 7 7. sinh ; tnh ; coth ; sech ; csch e. e 9. e. 0. cosh. cosh ( ). sech t tn h t 6. sech t t t tnh t 7. coth z z 9. = (sech u tnh u)(ln sech u). tnh. ;. ( ) 7. tnh u u. (u ) tnh (u ) 9. coth t t. sech ln. u. tnh z z 0. (csch u coth u)(ln csch u). coth. ; t coth t. sech ln. u. sec 6. sec, 0 p 7. () (tn (sinh ) C) sech (sin (tnh ) C) sech. sech C sech 9. coth C coth 0. tnh ln ( ) C tnh. cos h C. cosh C. sinh ln C. sinh ( ln ) C. 7 ln cosh 7 C 6. ln u sinh C 7. tnh C. coth ( ) C 9. sech t C 0. csch (ln t) C. ln (/) ln (/) ln ln (/) e e.0 6. e e /. (e e e e ) (/) ln (99/) ln.9 6. p 6. p 6. ln p. 6. () 6/ sinh b 6. () If g() f () f (), then g() f () f () g(). Thus, f () f () is even. If h() f () f (), then h() f () f () f () f () h(). Thus f () f () is o.

5 690 Aitionl Answers Even prt: e e cosh prt: e e sinh 66. () If f is even, then f () f () f () f () f () f () f () f () 0 If f is o, then f () f () f () f () f () f () f () f () 0 f () 6. () s k s is irecte towr the origin. s k s is irecte w from the origin. 69. sech () 70. 6p ln 6 p (c) A(0) 0, C 0, u A(u)

FP3 past questions - conics

FP3 past questions - conics Hperolic functions cosh sinh = sinh = sinh cosh cosh = cosh + sinh rcosh = ln{ + } ( ) rsinh = ln{ + + } + rtnh = ln ( < ) FP3 pst questions - conics Conics Ellipse Prol Hperol Rectngulr Hperol Stndrd