teorie conics

8/13/2019 teorie Conics

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QUADRATIC RELATIONS (CONICS)

DAY 1

Relations & Functions

Quadatic Relation

any relation that can be written in the form2 2

0Ax Bxy Cy Dx Ey F+ + + + + = , A, B, and C cannotall equal 0. In Math 30P, we look at relation where B ! 0.

Conic o Conic Section

e"ery quadratic relation #$rimary % de&enerate' can be hown a the interection of a $lane and a

ri&ht circular cone or cylinder.

(ouble)*a$$ed Cone Cylinder #cone with "erte+ off to infinity'

Pa&e M30P -P C 3 Conic

&enerator

"erte+

"erte+ an&le

a+i a+i

&enerator


2/8

Circle

$lane i $er$endicular #at a /0 ' to a+i #dotted line i a+i'

Circle.m$& i a"ailable

lli$e

$lane i between $er$endicular to a+i #circle' and the &enerator

1 can only interect one na$$e #dotted line i a+i, olid line are &enerator'

li$e.m$& i a"ailable

Parabola Parabola.m$& i a"ailable

$lane i $arallel to &enerator

y$erbola y$erbola.m$& i a"ailable

$lane i between &enerator and $arallel to a+i #include bein& $arallel to a+i'

Pa&e 2 M30P -P C 3 Conic


3/8

!isual E"a#$les o% Conic Coss Sections Conic ideo.m$& i a"ailable

Pa&e 3 M30P -P C 3 Conic


4/8

aa'olas

Math 20

quadratic function

tandard 4orm5 y ! a#+ h'2

6 k

Math 30

quadratic relation

tandard 4orm5 y ! a#+ h'26 k 'eco#es

y k ! a#+ h'2

"erte+5 #h, k'a 7 0, then $arabola o$en u$a 8 0, then $arabola o$en down

OR

tandard 4orm5 + h ! a#y k'2

"erte+5 #h, k'a 7 0, then $arabola o$en ri&ht

a 8 0, then $arabola o$en left

9eneral 4orm

A+26 (+ 6 y 6 4 ! 0 OR Cy26 (+ 6 y 6 4 ! 0

1 either A or C equal 0 #AC ! 0'

Pa&e : M30P -P C 3 Conic


5/8

+am$le5

. (etermine5

a. "erte+

b. direction of o$enin& and tretch #a'c. ketch

d. domain and ran&e

e. + and y)int#'f. equation of a+i of ymmetry

i. y ; ! 2#+ 6


6/8

ANS+ ! 3y2

5 #0, 0'

3. (etermine equation of the followin& $arabola in both form.

a. "erte+ i #3, :'@ $ae throu&h #, 2'@ o$enin& u$ or down

ANSy : ! a#+ 6 3'2, $lu& in #, 2' to &et a !3

2

y : !3

2 #+ 6 3'2and 3+26 ;+ 6 2y 6 / ! 0

b.

Method Method 2

ubtitute $oint find a by tretch

a#y 6 :'2! + u$ , ri&ht


7/8

b. elli$e ANSA 8 0 #include circle'

c. $arabola ANSA ! 0d. hy$erbola ANSA 7 0

3. 4or what "alue#' of C i Cy26


8/8Pa&e ; M30P -P C 3 Conic

teorie conics

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