Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Identify the Conic With a Given Polar Equation

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Polar Equations Of Conic Sections

Given the polar equation, identify the conic section.

$r=\frac{14}{7-7\cos\theta}$

Possible Answers:

Hyperbola

Ellipse

Parabola

Correct answer:

Parabola

Explanation:

Recall that the polar equations of conic sections can come in the following forms:

$r=\frac{ed}{1\pm e \cos(\theta)}$

$r=\frac{ed}{1\pm e \sin(\theta)}$ , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity.

0<e<1 will give an ellipse.

e=1 will give a parabola.

e>1 will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by .

$r=\frac{14}{7-7\cos\theta}=\frac{2}{1-\cos\theta}$

Now, for the given conic section, e=1 so it must be a parabola.

Report an Error

Example Question #22 : Conic Sections

Given the polar equation, identify the conic section.

$r=\frac{16}{8+4\cos\theta}$

Possible Answers:

Parabola

Hyperbola

Ellipse

Correct answer:

Ellipse

Explanation:

Recall that the polar equations of conic sections can come in the following forms:

$r=\frac{ed}{1\pm e \cos(\theta)}$

$r=\frac{ed}{1\pm e \sin(\theta)}$ , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity.

0<e<1 will give an ellipse.

e=1 will give a parabola.

e>1 will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by .

$r=\frac{16}{8+4\cos\theta}=\frac{2}{1+\frac{1}{2}\cos\theta}$

Now, for the given conic section, 0<e<1 so it must be an ellipse.

Report an Error

Example Question #31 : Conic Sections

Which type of conic equation would have the polar equation $r = \frac{1}{ 3 + \sqrt8 \cos \theta}$ ?

Possible Answers:

Ellipse

Not a conic section

Circle

Parabola

Hyperbola

Correct answer:

Ellipse

Explanation:

This would be an ellipse.

The polar form of any conic is $r = \frac{ep }{ 1 \pm e \sin \theta}$ [or cosine], where e is the eccentricity. If the eccentricity is between 0 and 1, then the conic is an ellipse, if it is 1 then it is a parabola, and if it is greater than 1 then it is a hyperbola. Circles have eccentricity 0.

To figure out what the eccentricity is, we need to get our equation so that the denominator is in the form $1 + e \sin \theta$ . Right now it is $3 + a \sin \theta$ , so multiply top and bottom by $\frac{1}{3}$ :

$\frac{1}{3 + \sqrt 8 \cos \theta} * \frac{\frac{1}{3}}{\frac{1}{3}} = \frac{\frac{1}{3}}{1 + \frac{\sqrt8 }{3}\cos \theta }$ .

Now we can identify our eccentricity as $\frac {\sqrt 8 }{3} \approx 0.942$ which is between 0 and 1.

Report an Error

Example Question #11 : Identify The Conic With A Given Polar Equation

Which type of conic section is the polar equation $r = \frac{6}{2 -2 \sin \theta}$ ?

Possible Answers:

Hyperbola

Parabola

Not a conic section

Ellipse

Circle

Correct answer:

Parabola

Explanation:

All polar forms of conic equations are in the form $r = \frac{ep}{ 1 \pm e \sin \theta}$ [or cosine] where e is the eccentricity.

If the eccentricity is between 0 and 1 the conic is an ellipse, if it is 1 then it is a parabola, if it is greater than 1 it is a hyperbola. Circles have an eccentricity of 0.

We want the denominator to be in the form of $1 - e \sin \theta$ , so we can multiply top and bottom by one half:

$\frac{6}{2 -2 \sin \theta} * \frac{\frac{1}{2}}{\frac{1}{2}} = \frac{3}{1 - 1 \sin \theta}$

The eccentricity is 1, so this is a parabola.

Report an Error

Example Question #15 : Identify The Conic With A Given Polar Equation

Which type of conic section is the polar equation $r = \sin \theta$ ?

Possible Answers:

Circle

Parabola

Hyperbola

Ellipse

None of these

Correct answer:

Circle

Explanation:

Although it's not immediately obvious, this is a circle. One way we can see this is by converting from polar form to cartesian:

$r = \sin \theta$ multiply both sides by r

$r^2 = r \sin \theta$ we can now replace r^2 with x^2 + y^2 and $r \sin \theta$ with :

x^2 + y^2 = y We can already mostly tell this is a circle, but just to be safe we can put it all the way into standard form:

$x^2 + y^2 - y \enspace \enspace \enspace = 0$ complete the square by adding $(-\frac{1}{2})^2 = \frac{1}{4}$ to both sides

$x^2 + y^2 - y + \frac{1}{4} = \frac{1}{4}$ condense the left side

$x^2 + (y - \frac{1}{2}) ^ 2 = \frac{1}{4}$

Now this is clearly a circle.

Report an Error

View Pre-Calculus Tutors

Rhys
Certified Tutor

Portland State University, Bachelor of Science, Microbiology. Arizona State University, Doctor of Philosophy, Microbiology.

View Pre-Calculus Tutors

Momeena
Certified Tutor

State University of New York at New Paltz, Bachelors, Mathematics & Elementary Education. State University of New York at New...

View Pre-Calculus Tutors

Colton
Certified Tutor

Texas State University-San Marcos, Bachelor of Science, Mathematics.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Washington DC, Reading Tutors in Philadelphia, SSAT Tutors in Seattle, GMAT Tutors in Dallas Fort Worth, Math Tutors in New York City, Algebra Tutors in San Francisco-Bay Area, Math Tutors in Seattle, MCAT Tutors in Phoenix, English Tutors in Atlanta, English Tutors in Los Angeles

Popular Courses & Classes

SSAT Courses & Classes in Denver, Spanish Courses & Classes in Phoenix, SAT Courses & Classes in Seattle, MCAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC, SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in New York City, MCAT Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in Boston, SAT Test Prep in Miami, ACT Test Prep in Seattle, GMAT Test Prep in Philadelphia, SSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Philadelphia, GMAT Test Prep in Phoenix, SSAT Test Prep in Houston, ISEE Test Prep in Denver, ACT Test Prep in Washington DC

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Precalculus : Identify the Conic With a Given Polar Equation

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #11 : Polar Equations Of Conic Sections

Example Question #22 : Conic Sections

Example Question #31 : Conic Sections

Example Question #11 : Identify The Conic With A Given Polar Equation

Example Question #15 : Identify The Conic With A Given Polar Equation

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: