12th - CHAPTER 10 CONIC SECTIONS AND POLAR COORDINATES 10.1...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHAPTER 10 CONIC SECTIONS AND POLAR COORDINATES 10.1 CONIC SECTIONS AND QUADRATIC EQUATIONS 4. 312‘; :> 413:2 :> 1):. :focusis(0_., l». I.— ) ,dircctrix is y : — l». I.— [C |—‘ ”' “L‘s? Y—f—E —> 49-8 p—2; focus is [0, —2}, dircclrix is y = 2 23. 6x3—9y3254 2 xii—£21 :;> c: V303 — b3 : \f9— f3: 32. 39—3)? :3 :> —x3: I :> c: VaB—b2 : «v.33 — I : 2; asymptotcs are 3! : ; VG): 42. (a) — = 1 :5» center is (0, 0), vertices are (0,5) and (0, —5);c = V 33 — I.)2 = V/l— = 4 2:» foeiare (0, 4) and (0, —4) ; therefore the new center is (—3, —2), the new vertices a1'e(—3_. 3) and (—3, —7), and the new foci are (—3, 2) and (—3, —6) x3 ,2— 50. 7—. — (— l_. 0) and (1, 0); therefore the new center is (3,4), the new vertices are (3 ; V5.4 (it-313 , 2_ ., —(3 —4) —l are (2, 4) and (4,4); the new equation is 71. 10.2 CLASSIl-"YING CONIC SECTIONS BY I‘ICCENTRICITY l 2:» center is (0.0), vertices are (V/Efi) and (—V/Efi) ;c = \, /32_b2: x’_—1:]::> foeiare 9. Foei:[0,;3],e 0.5 »c 3anda E 6 »b3 36—9 27 20. UsingPF:e-PD,wehave V(x—4)3—y3= |x—9| 2:» (x—4)2—y2= zg‘LxB—mx—sn=>ng—ygzzo25x3—9y32130m§—%=1. 1 s \r an the new foei 23 y3—3x~=3:.~ “Ti—x32] :czv’aB—tfi =\f3—l=2:>e=§=%;asymptotesare \} y = _ V/gx, F[0_. ; 2] ;direetriees are y = 0;: — 2 _3 (vs) 37.Focus(—2,0)andDirectrixx —.]3 »c ae 2andg 13 »e2 »e PF—ZPD V50: 2)? (y (DB—2x 33 (x :3 y3—4(x 33]? x3 4): y? 24(x3 x 3.):2 ye: 32:»):2 :12] 10.3 QUA DRA TIC. EQUATIONS AND ROTATIONS 12. 232 — 4.9X)’ — 3y2 — 4x = 7 2:» B2 — 4AC = (—4.9)2 — 4(2)(3) = 0.0] '9 CI 2:» Hyperbola 15. 6x3 — 3xy — 2y? —17y— 2 = 0 2 B2 — 4AC = 32 — 4mm) 2 —39 < 0 :» Ellipse _ q_ . I 22. cot 2a- % — 713 » 2n- 27” » a %;tliereforex= x’ cos a— 5” sin _ x _ . fi fi y:x’slna—}Hcosa::>x=.X’—l%}" y=l2—'x’—% I) X’ ‘f)”)(‘-.3x’ éy’) ifjd=l=>4rfl=l I_ ma => 3(%x’—H—’?y)2—2 G(. l 2:» Parallel horizontal lines 10.4 CONICS AND PARAMETRIC EQUATIONS; THIC CYCLUID 7. x=—sect,y=tant,—%<t<% I) 2:» secgt—tangtzl 2:» xg—y‘zl 12. x: sinht,y=2cosht,—oo<t<oo fl 2:» 4COSl12l—4Slllh3l24 3333—31224 3' 32—: -4 4. (a) (3,? — Zmr] and (—3, 57” — Enrr] , n an integer y (b) (—3, g — anr] and (3, 57" — EnTr] , n an integer (c) (3, — i — 2n7r] and (—3, 3?” — 211a] , n an integer (d) (—3, — g — inn] and (3, 37” — 211a] ,n an integer I Hum ta.—ml o o 6. (a) x : VG cos § : l, y : p6 sin § : l 2:» Cartesian coordinates are (l, l) (b) x — 1 cos 0 — l, y — 1 sin 0 — 0 -*» Cartesian coordinates are (l, 0) (c) x — 0 cos — 0, y — 0 sin — 0 -*» Cartesian coordinates are (0.0) (d) x = —\,/§cos = — l, y = —\,/3 sin 2 —1 2:» Cartesian coordinates are (— l, — l) (e) x = 3 cos 5‘; = 3g? , y = 3 sin 5‘; = 2:» Cartesian coordinates are (355, — (f) x = 5 cos (Ian—1 31] = 3, y = 5 sin (tan—l = 4 2:» Cartesian coordinates are (3.4) (g) x = —1 cos Trr : l, y = —1 sin "in = 0 2:» Cartesian coordinates are (1,0) (ll) x = 2V 3 cos = —\,/3, y = 2V 3 sin = 3 ::> Cartesian coordinates are (—V/g, 3) 13. E 3 31. 13 : 1 :> x2 — y? : 1, Circle with center C : (0,0) and radius 1 Six—19:3 2:» roosfi—rsinfiz'j 10.6 GRAPHING IN POLAR COORDINATES 10. sinfir — 9) = sin F) = 13 2:» (1".TI' — 9) and (—r,?r — 9) are on the graph when (139) is on the graph ::> symmetric about the y—axis and the x—axis; therefore symmetric about the origin 19.62%31'213(1,%:];6‘:—%:>r:_] 2’(“>—%J;9=%w=—I244%); 62—3?”::,1.:]:> ]!_T,r]; J_$_ o. 1—da—2005_6‘, Slope = r’siné‘ircosé‘ _ 2005235in3ircos3 r'cosfl—rsinfl _ Zoosficosg—rsiné' JI' 2:» Slope at (l, . Zoos[— sin[— “:1 H—iJcos[— Slope at( 1’ l5 2005L— cos L—E)—E—]JsinL—;) 31r isNOSE]sin(%jn—ncos(‘wj _ I J J J 1—1 510 eat I. T p ( ' 4 5 -(—l]sin(37"' :1; 4 Slope at (I, 3”] is 2 cos (— sin (— tilicos E— l 24. (a) (b) 26. 1‘ 2 sec 0 r b) rcosl’} 2 x cos 5‘ U 35. (x5) :4sinl’) => szsino => u:%,%zmints of intersection an: _. and _. . The points (VG, — and (VG, — alt found by graphing. ...
View Full Document

Page1 / 5

12th - CHAPTER 10 CONIC SECTIONS AND POLAR COORDINATES 10.1...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online