Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Polar Equations for Conics: Identifying Conics and Their Directrixes, Exercises of Calculus

Aligarh Muslim UniversityCalculus

Polar equations for various conics, including hyperbolas and ellipses, along with the position of their directrixes. Students are asked to identify the type of conic and the location of the directrix based on the given polar equation.

Typology: Exercises

2012/2013

Uploaded on 02/11/2013

somitra-dave
somitra-dave 🇮🇳

4.7

(3)

55 documents

1 / 5

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Polar Equations for Conics
Identifytheconicthatthepolarequationrepresents.Also,givethepositionofthedirectrix.
1) r=9
1-3cosθ
A) hyperbola,directrixperpendiculartothepolaraxis3 leftofthepole
B) ellipse,directrixperpendiculartothepolaraxis3 leftofthepole
C) ellipse,directrixperpendiculartothepolaraxis3 rightofthepole
D) hyperbola,directrixperpendiculartothepolaraxis3 rightofthepole
2) r=2
2+2sinθ
A) hyperbola,directrixparalleltothepolaraxis1 abovethepole
B) parabola,directrixparalleltothepolaraxis1 abovethepole
C) hyperbola,directrixperpendiculartothepolaraxis1 rightofthepole
D) parabola,directrixperpendiculartothepolaraxis1 rightofthepole
3) r=2
4-2sinθ
A) ellipse,directrixperpendiculartothepolaraxis1 rightofthepole
B) ellipse,directrixparalleltothepolaraxis1 abovethepole
C) ellipse,directrixparalleltothepolaraxis1 belowthepole
D) ellipse,directrixperpendiculartothepolaraxis1 leftofthepole
4) r=6
3-4cosθ
A) ellipse,directrixisperpendiculartothepolaraxisatadistance3
2unitstotherightofthepole
B) hyperbola,directrixisperpendiculartothepolaraxisatadistance3unitstotherightofthepole
C) hyperbola,directrixisperpendiculartothepolaraxisatadistance3
2unitstotheleftofthepole
D) ellipse,directrixisperpendiculartothepolaraxisatadistance3unitstotheleftofthepole
Discusstheequationandgraphit.
5) r=6
3-3cosθ
r
-5 -4 -3 -2 -1 1 2 3 4 5
5
4
3
2
1
-1
-2
-3
-4
-5
r
-5 -4 -3 -2 -1 1 2 3 4 5
5
4
3
2
1
-1
-2
-3
-4
-5
pf3
pf4
pf5

Partial preview of the text

Download Polar Equations for Conics: Identifying Conics and Their Directrixes and more Exercises Calculus in PDF only on Docsity!

Polar Equations for Conics

Identify the conic that the polar equation represents. Also, give the position of the directrix.

  1. r = 9 1 - 3 cos θ A) hyperbola, directrix perpendicular to the polar axis 3 left of the pole B) ellipse, directrix perpendicular to the polar axis 3 left of the pole C) ellipse, directrix perpendicular to the polar axis 3 right of the pole D) hyperbola, directrix perpendicular to the polar axis 3 right of the pole

  2. r = (^2) + 22 sin θ

A) hyperbola, directrix parallel to the polar axis 1 above the pole B) parabola, directrix parallel to the polar axis 1 above the pole C) hyperbola, directrix perpendicular to the polar axis 1 right of the pole D) parabola, directrix perpendicular to the polar axis 1 right of the pole

  1. r = 2 4 - 2 sin θ A) ellipse, directrix perpendicular to the polar axis 1 right of the pole B) ellipse, directrix parallel to the polar axis 1 above the pole C) ellipse, directrix parallel to the polar axis 1 below the pole D) ellipse, directrix perpendicular to the polar axis 1 left of the pole

  2. r = 6 3 - 4 cos θ

A) ellipse, directrix is perpendicular to the polar axis at a distance 32 units to the right of the pole

B) hyperbola, directrix is perpendicular to the polar axis at a distance 3 units to the right of the pole C) hyperbola, directrix is perpendicular to the polar axis at a distance 3 2

units to the left of the pole

D) ellipse, directrix is perpendicular to the polar axis at a distance 3 units to the left of the pole

Discuss the equation and graph it.

  1. r = (^3) - 36 cos θ

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

PreCalculus

  1. r = 9 3 - sin θ

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

  1. r = 3 2 + 4 sin θ

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

Find a polar equation for the conic. A focus is at the pole.

  1. e = 1; directrix is parallel to the polar axis 2 above the pole A) r = 2 1 + sin θ

B) r = 2 1 + cos θ

C) r = 2 1 - cos θ

D) r = 2 1 - sin θ

  1. e = 1 2

; directrix is perpendicular to the polar axis 2 to the left of the pole

A) r = (^4) - 28 cos θ B) r = (^4) + 24 cos θ C) r = (^4) - 24 cos θ D) r = (^4) + 28 cos θ

Convert the polar equation to a rectangular equation.

  1. r = (^2) - 24 cos θ

A) x2^ = - 4y + 4 B) x2^ = 4y + 4 C) y2^ = - 4x + 4 D) y2^ = 4x + 4

  1. r = 6 2 - 2 sinθ A) x2^ = 6y + 9 B) x2^ = - 6y + 9 C) y2^ = 6x + 9 D) y2^ = - 6x + 9

Answer Key

Testname: 15_POLAR_EQ_CONICS

1) A

2) B

3) C

4) C

  1. parabola; directrix perpendicular to the polar axis 2 units to left of pole focus (0, 0), vertex 1, π

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

  1. ellipse; directrix parallel to the polar axis 9 units below pole center 98 , π 2

vertices 9 2

, π 2

, 3 π 2

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

Answer Key

Testname: 15_POLAR_EQ_CONICS

  1. hyperbola; directrix parallel to the polar axis 3 4

unit above the pole

vertices 1 2

, π 2

, 3 π 2

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 r

5 4 3 2 1

  1. A
  2. C
  3. D
  4. A
  5. D
  6. B
  7. D
  8. B