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Unit 7 Conics Key

The document provides a review of conic sections, including ellipses, parabolas, and hyperbolas, detailing their centers, vertices, foci, directrices, and equations of asymptotes. Specific examples are given for each conic type, including calculations for their properties and equations. The review serves as a study guide for identifying and graphing conics in precalculus.

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43 views4 pages

Unit 7 Conics Key

The document provides a review of conic sections, including ellipses, parabolas, and hyperbolas, detailing their centers, vertices, foci, directrices, and equations of asymptotes. Specific examples are given for each conic type, including calculations for their properties and equations. The review serves as a study guide for identifying and graphing conics in precalculus.

Uploaded by

ao80000
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Precalc AB Unit 7 Review (Conics) Let's start by identifying and graphing each conic. Find the center, focus/foci, vertex/vertices, ‘equations of asymptotes, and directrix for each, where applicable: Ellipse! Facieg 0 center: (0,0) vertices: CO,a) (0,-2) co-vertices: (15,0) (-4,0) Foci: (0,1) Co,-1) Porabola! Facing C$ vertex : (0,0) focus: C1,0) divectriz: x=-] focal width = 4 2.2 _ voelal Facing 3. . yta=s Hype 1 Se | te (yay +1 )e sesh - B= Cg-n)*s 4 f 4 4 4 center: (0,1) sas: Cu) Gy) LLL = (ye | Ue 9 a foci: (85,1) | L4 asl asymptotes 2 | ps2 ye taxel +} aaa or yale tateo ll CzOrh Saas Cha 144 Coe a a 4 x ty? t+ 6x —4y-51=0 Cire] yr ox + y= yt lex te 4 + dye Ge syed (x43ye Cy-a = center: (-3,a) radius: & Paral olal ae 5. Pome m0 x axel = By-4Ae 1 ones By 48 ptt tt (a- 72 BCy-&) | vertex > C1, &) Sr dp=% focus; C48) | er divectrix: 45 focal width. 3 Now, write the equation of the conic described. 6, Anellipse with center ses on the major axis at (-3, 3) and (7, 3), ae minor axis fenth of (n= a" C > bel as conker, por (a ‘need 7. Circle with center (1, 2) and the point (1, 4) lies on the circle. canter: (1,2) radive: 4 ailtemate way to Find radius: === re one » +a-n re oe + oo Sm ost sae ret 8. Hyperbola with vertices at (0, 2) and (2, 2). The foci are at (-1, 2) and (3, 2). 5¢ center: (1,2) za a. zor \ CAzce+o ys i +b es or Le pals 9. Parabola with vertex (0, 2) and directrix at y = -2. TD Vertex: (02) = e=4 X = Mo(y-2) 4e=

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