chapter · d-diedm v. vertex definition apwnbok iothesetof points equidistant fromthe focus ad...
TRANSCRIPT
chapter lb
Conidsi
Parabolas @±I¥U¥
:•¥-*•
.
F-focus
D - Diedm
V . vertex
Definition apwnbokiothesetof points equidistantfrom The Focus ad Directory .
According 6 definition
(b)
±.ae,0 )
Distance from@,
*to ( x , g) =
@,
° ) to (× , I )
Standardequation of
Parabolap 1 beta foal bnght
and ( h , K) be he vertex .
then¢×-
his4.p(y - k)
in other form
y = Effort
Example-
Gnpkifd3j.Ekx-DFh-ysieeyanporent-iosqvuethenthegnfshofsensrightorbftt8I-7Eneethismultfdieusnegntwethen.egeaphofonsbft.Vertex@si8I-4p-2-pfoeus.2unitslefttotheiH.EI.r
.±m⇒*laetusrdm
Ellipse•
C• Matnaxis. us
F I,{ Fu
EtlipsewitncentucFoci Fiadfuadvertise ,sdVu
Btwdmdeqmtrmof Ellipse :X .hj+(y-h)÷.
"
Example Iwrite the equation ofthe ellipse given by :X H 4 y2 - 2×+24 y
t 33 = o
tnstmdmd form¥y?t@¥o÷Group mills :
X 2- 2 × + 4 y he 24 y= - 33
a- Complete the square for both
priests .
(172×+12)+4(y2+6yt⇒=-33+1+3-6
E -1) 4 4 ( yt 3) ¥ 4
3 - Dini de both sides by The eostwt
Turn .
@- 1 )2+ 4 ( y t 35=4
÷¥ test 1
Example 2 ×¥'tt¥I= I
Eideqntron of an ellipse with
foci ( 2,
, ) and (4, 1) and vertex ( 0, D
V • . .
=.fi#.CF :C=(3 ,
i) since lotus midpoint
of F ,and Fu
A =3 since dshee between Vaud C 's 3
ar=9 we must find b
C = 1 since disthe from F to C 's 1-
e. T.at#=l3
'Ts¥Ipfit¥5ai
Hyperboles
§¥ .
ouster
F , • .
transiiusegqkyis rv
F Foeci
j Vertex- complinsty al is
- Transverse axis
guide vet mgle
Stmdmd eqmtr on forHypnboh .
@- h ) 2- ( y -142¥be
Exmfdaphthe eqmt . on
6¥ . ¥ a
Find : ate : ( 2 ,° )
conjugate axis : X = 2
tnnsvens axes ; ya 0
Vertices : ( 0,0 ) ad ( 4,0 )Foci : (2 - Bna
,o ) ad (2+59,0)
eqntuns of asymptote :
g- ± EEA
See how t got all theseplus
@-
zji,
- Is "
e¥tr¥÷i⇒÷o,
@-25-(7-0)"=1 a=2 Immense
TT
btsconfdity•=,
Comers of guided1 trmgk .
E 1 @,s ) ,@,s ) ,(o ,- 5)
altar .¥29,0)E1 ( atkqo)
- (4-5)a-d-
.mn enter
Example 2
hhite the eqmtr on 9y±x±6x = to
as a shdmd form of a
Hyperbole .
I - Group sme wilds together ,
9y2 - x2- 6 × = 10
2- eofoleto the square forboth
mills .
9 y'
. i (xht 6 x + I) = lot
#-)9up - (X +35=10 - 9 = 1
3 Diwde by constnt terms .
÷e¥÷fi¥:i's
e- FE FE= Nt
3
Example 2 continues . • certes ( ' 3,0 )
# . ( xe3P=| Virtues ,⇒tsp )
+ •Focif3N÷ )q HE ↳n⇒÷÷i*i•f(Aspfhtsy - tzx - 1
ad yatzx -11