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## section 9.3 the ellipse

by: Emmaline Murphy

19

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6

# section 9.3 the ellipse MAC 1140

Emmaline Murphy
FSU

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9.3 notes for precal
COURSE
Precalculus Algebra
PROF.
David Ekrut
TYPE
Class Notes
PAGES
6
WORDS
CONCEPTS
precal
KARMA
25 ?

## Popular in Mathematics (M)

This 6 page Class Notes was uploaded by Emmaline Murphy on Tuesday March 1, 2016. The Class Notes belongs to MAC 1140 at Florida State University taught by David Ekrut in Spring 2016. Since its upload, it has received 19 views. For similar materials see Precalculus Algebra in Mathematics (M) at Florida State University.

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Date Created: 03/01/16
'? ntlfi6r fb (-q, hr,,o lr,*niu, ? Mgtx' &xtt \s X-aYtt r.€iro) oFy \.[_z F.ltnor Aillt is Y -q,xls b2+ c?? olz = bQ = A2- (1. n.rrns Er,r,rpsp Definitiont-1.. ellipsisthesetofal,loi.nPs, {r,y},suehho.t the sofn thedi.stancestweetwopo'i,ncalled,efociof thelli,psconstant. The rnajor axisthe ari,s througfoci,. The rninor axastheo.ri,sraugth,centererpend,i,etothemajor *ri,s. The verticeofheelli,pse theointwhere thelli,'intersectsmajararis. 2.EeuarroNs (*-hl)'-ik)- k)':,1|(*-hh)z ,(y-k)'_,, n -(a-V---;;-^ o' -(y-a'-- Axisr x- qx ts Y-ax15 a)b, relatibetween 6r-- q'- c2 b2, a2 - c2 a,b,antc Center V) Ch, E) Ch, Foci (vt *C, k) (h, Y+ A Ih 'At K) Ch, v:4 Vertices (h+o, k) (-v\ + e) ,V (h- a, K) (h r K-q) Sketch Atov' ,--l L, rnr AV r) filho r v, Section Example2.L.Fi,ni|,uati,ofthcnni,epheibelow. Fo6: ;{ A') ,) x' Y- f -F 1 x 1--. 7l V: -b'o a' \ .. _)< A=4 lt= 2 XZ , Y2 : + tn6\\0r 4 rh, o(rs 2.2Fi,nthequati.anthcani,caphed' Example 1 (x -h)' cy- k)= lo 0r' - *t L\3,-z (x -3)' (q+e, 1o2' I qe a,=3 b r l rnlh0 y : (x -3)= ct--A-i )-*-- S -*-- I A I u-sT (Y+2/ l--t : I I _ __3 4tt-1.1 bo= o3- c* b'=b2* 1' Sect9.3 aO, 3t0* lb Example 2.Writeusilowecnsr)thformuforg'nthe elwithcenter .u,u""""s"m* ""aucen"""?r,|'ti"'**'fu' o = 3b = | =Tr.{,";#=o,u'*,*! Example 2.Findthequatioftheelli.pse watth and, and,=; '' 3U(l-#} foci {-1,2) {3,2) - rr'!+'.\^,^-.. ,*l t)e+ (v*rte u* - q tri,',,'f = -q s-=l - , b^=5 q- b*= 4 Example2.5. "#i"* # c '--lb U^2*U dl= 4 x-0 elli,pse2/,i,r2r., t\2oci,,rtimajoraris,dm,inor aforhe ceffr;"'l(t, 4)lq## . +1)' {- 2)2 16 -0 1-I"o = t = 2 3:= .l 1t-''r-r(\-t,K1(r) .- \l'r,a (_l,{r)e(-t,"p) \__ t' 1{r {ut' Il,l;fi* )ac- \,2.,,rre) 1. Spclloru 9.2 Tnn PlRnror,a Definition L.l.A parabola isthe setaf allpoi,ntsP : (r,g), thatare equ,id,istant .froma fisedpoi,ntcalled tlrecus and afined li,ne called directrix. 2.EeuauoNS,a)0 Equation Vertex IFocus IDirectrix :4a(r (v - k)' - lt) (v-k)':-4atr-tt\ X= h+a :4a(y (* - h)' - k) .VTV PIY (*-h)':-a"(y-k) X= K+r'l 4+& +5 Example2.1.Sketch thep,,'Y':;'r1t., (x n)'. <a61-4 (h, a)- Q,o) x2 --4a (v) (\>o 4ctt=-C=j \$=-* Example2.2.Find, the eofthearabod*rn"abebw. U-a)'= 4(t+3 j v&r.!ex: c \,e (V-Q'= 4a0-t, 6r-l^- 4a(x+t -4 -+c?,0 (o-;)a= 4a(-A+4 L'"hcn Ca)' = 4 6L,Ct) ",1:-. 0 /:4a-i- tzi - Example2.3.Fi,nd equatiofthearabouitlfocus1,-zand ueratr (11). 'PtvedYtx (x-h)" , ",(-h)n = - +a(V- o kt,,ri({} (x-D{= : * la cvv - r) ****f-f _+I_ !l[Ltuu It5.t,,(h,Y- =(t,-2) a=3) Example 2.Findtheequatiotheparabowi,th (-r, (1-2). focus -2)anduerter at 4a{x- h) .i (x rt ii (x*!) ((u:t ---? Section 3 Example2.5Fi,nd,equat'ofonearabaw'ituerter1-2)anddi,rectri,r ,-rr. I I (9 -v)' = -a(x*h) I (v+r)'= +r) I -rbCx i Example 2.6.ndtheequatiofn,earabowi,foeus-1,-Z)and,;i,rectri,r U:3. I Dir v€l'ttr=(-l,i) - I (x -a A -h)*= - 4a (v -r) t.J\ (x+r)a= _t}(y-i) parabola r2:6ale2.7Fi,nd,focus,i,reanduerter of wi,theequat'ion h r 4 q-h):=2 +alv-?, r..\ Y{r1 ry{a,o) \J / (x- -o)- *-+:- 0)^ = b (v 4et - b _ f - Drrr frcw.r, (o , ?) 7 L cirr-- Y=- ,Z u =37 Example2.8Fi,ntlfacus,,irectrii'a\d thefiarabotaheequation 2(A+2)2:*+3 ( - 2) vrv*Lx y+ 3 2, #(vt2)r= * tq, -2) Fcr,.,ts (y+ 1, (o +*") -# v\vecrY = * {= x ,= *a Example 2.9.,nd,focus,,i,rectaer-terthearabola wi,equat'ion =o() (Y+Z)2--2r*3 fl::tr -v\^ -- - 1 a (x-r,) ^r=rr,*l I C./ 'ir"I\.x 6t *e)'. _Jy+?,(y*;)r_ *,{y_i) v{t?(x - (A u\ -4a -;" 7 ,-d) = ff: i

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