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Exercises on Parabolas, Circles, Ellipses, and Hyperbolas, Assignments of Calculus

Iowa State University (ISU)Calculus

Exercises on various conic sections including parabolas, circles, ellipses, and hyperbolas. The exercises cover topics such as equations, graphs, vertices, asymptotes, directrices, eccentricities, and foci. Students can use this document as a study resource for understanding conic sections and preparing for exams.

Typology: Assignments

Pre 2010

Uploaded on 09/02/2009

koofers-user-f12
koofers-user-f12 🇺🇸

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Exercises 12.6
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Download Exercises on Parabolas, Circles, Ellipses, and Hyperbolas and more Assignments Calculus in PDF only on Docsity!

Exercises 12.

27. r= 4 sin (θ).θ).).

 

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   

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         

       

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   

 

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  4 8 16.

2 cos 4.

cos 4.

cos 4.

cos

cos 1 sin 0 cos.

cos - cos cos sin sin

cos

Parabola.

4 cos.

cos 4.

1 cos

r

Circlewithcenterat(θ).0,2)andradius 2.

4 sin.

2 2 2

2 2

2

2

2

2 2 2

2 2

2

2 2

2 2

2 2

2 2

2

x y x x

r x

r x

r r

r r

r r

r

r

y x

y x

y x

x y x x

r x

r x

r r

r r

x y

x y y

x y y

x y y

r r

 

 

Asymptotes

Vertices

Center at

Hyperbola.

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2 2

2 2

y x

y x

y

x

y

x

x y

x y

x x y

x x y

x x y

x

y

  

  

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 

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     

a

c

Eccentricity e

0 , 2 2 0 , 0 ,and 0,-2,-2 (θ). 0 , 4 ).

a 4,b 12 2 3.

Foci

Endpointsofminoraxis(θ).0 12 , 2 ) (θ). 2 3 , 2 ), (θ).0 12 , 2 ) (θ). 2 3 , 2 )

Vertices(θ).0,- 2 4) (θ).0,2),and(θ).0,- 2 - 4) (θ).0,-6).

Centerat (θ).0,-2)

Ellipse

sin.

2 6 sin.

2 sin 6.

2 sin 6.

2 sin

2 2 2

2 2

2 2

2 2

2 2

2 2

2 2 2

2

2

c

c a b

and

x y

x y

x y y

x y y

x y y

x y y y

r y

r y

r r

r r

r r

r

r