Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Parametric Form

Study concepts, example questions & explanations for Calculus 2

Create An Account

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #43 : Parametric, Polar, And Vector

Convert the following equation from parametric to rectangular form:

$x=e^t, y=2\sin(t)$

Possible Answers:

$y=2\sin(e^t)$

y=x

$y=-2\sin(\ln(x))$

$y=2\sin(\ln(x))$

Correct answer:

$y=2\sin(\ln(x))$

Explanation:

To convert from parametric to rectangular form, eliminate the parameter (t) from one of the equations:

$t=\ln(x)$

Now plug this into the equation for y to get our final answer:

$y=2\sin(\ln(x))$

Report an Error

Example Question #561 : Calculus Ii

Given x=3t-6 and y=7t+9 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{7}{3}x+23$

None of the above

$y=23x+\frac{7}{3}$

$y=23x-\frac{7}{3}$

$y=\frac{7}{3}x-23$

Correct answer:

$y=\frac{7}{3}x+23$

Explanation:

Given x=3t-6 and y=7t+9 , let's solve both equations for :

$x=3t-6\rightarrow t=\frac{x+6}{3}$

$y=7t+9\rightarrow t=\frac{y-9}{7}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-9}{7}=\frac{x+6}{3}$

$y-9=\frac{7}{3}(x+6)$

$y-9=\frac{7}{3}x+14$

$y=\frac{7}{3}x+23$

Report an Error

Example Question #562 : Calculus Ii

Given x=2t+11 and y=11t+2 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y=\frac{11}{2}(x-11)-2$

$y=\frac{11}{2}(x+11)+2$

$y=\frac{11}{2}(x-11)+2$

$y=\frac{11}{2}(x+11)-2$

Correct answer:

$y=\frac{11}{2}(x-11)+2$

Explanation:

Given x=2t+11 and y=11t+2 , let's solve both equations for :

$x=2t+11\rightarrow t=\frac{x-11}{2}$

$y=11t+2\rightarrow t=\frac{y-2}{11}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-2}{11}=\frac{x-11}{2}$

$y-2=\frac{11}{2}(x-11)$

$y=\frac{11}{2}(x-11)+2$

Report an Error

Example Question #563 : Calculus Ii

Given x=t+3 and $y=\frac{1}{2}t-3$ , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{x-3}{2}-3$

$y=\frac{x+3}{2}+3$

$y=\frac{x+3}{2}-3$

None of the above

$y=\frac{x-3}{2}+3$

Correct answer:

$y=\frac{x-3}{2}-3$

Explanation:

Given x=t+3 and $y=\frac{1}{2}t-3$ , let's solve both equations for :

$x=t+3\rightarrow t=x-3$

$y=\frac{1}{2}t-3\rightarrow t=2(y+3)$

Since both equations equal , let's set them equal to each other and solve for :

2(y+3)=x-3

$y+3=\frac{x-3}{2}$

$y=\frac{x-3}{2}-3$

Report an Error

Example Question #51 : Parametric, Polar, And Vector

Given x=10-t and y=5t+3 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

y=53+5x

y=53-5x

y=5+53x

y=5-53x

Correct answer:

y=53-5x

Explanation:

Given x=10-t and y=5t+3 , let's solve both equations for :

$x=10-t\rightarrow t=10-x$

$y=5t+3\rightarrow t=\frac{y-3}{5}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-3}{5}=10-x$

y-3=5(10-x)

y=5(10-x)+3

y=50-5x+3

y=53-5x

Report an Error

Example Question #51 : Parametric, Polar, And Vector

Given x=8-3t and y=7-4t , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y=\frac{4}{3}(x-8)-7$

$y=\frac{4}{3}(x+8)-7$

$y=\frac{4}{3}(x-8)+7$

$y=\frac{4}{3}(x+8)+7$

Correct answer:

$y=\frac{4}{3}(x-8)+7$

Explanation:

Given x=8-3t and y=7-4t , let's solve both equations for :

$x=8-3t\rightarrow t=-\frac{x-8}{3}$

$y=7-4t\rightarrow t=-\frac{y-7}{4}$

Since both equations equal , let's set them equal to each other and solve for :

$-\frac{y-7}{4}=-\frac{x-8}{3}$

$-(y-7)=-4\left(\frac{x-8}{3}\right)$

$y-7=\frac{4}{3}(x-8)$

$y=\frac{4}{3}(x-8)+7$

Report an Error

Example Question #564 : Calculus Ii

Given x=7t-4 and y=2t+9 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{2}{7}(x+4})+9$

None of the above

$y=\frac{2}{7}(x-4})+9$

$y=\frac{2}{7}(x+4})-9$

$y=\frac{2}{7}(x-4})-9$

Correct answer:

$y=\frac{2}{7}(x+4})+9$

Explanation:

Given x=7t-4 and y=2t+9 , let's solve both equations for :

$x=7t-4\rightarrow t=\frac{x+4}{7}$

$y=2t+9\rightarrow t=\frac{y-9}{2}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-9}{2}=\frac{x+4}{7}$

$y-9=2\left(\frac{x+4}{7}\right)$

$y=\frac{2}{7}(x+4})+9$

Report an Error

Example Question #52 : Parametric, Polar, And Vector

Given x=2t-11 and y=-t+9 , what is in terms of (rectangular form)?

Possible Answers:

$y=9+\frac{x-11}{2}$

$y=9-\frac{x+11}{2}$

$y=9+\frac{x+11}{2}$

$y=9-\frac{x-11}{2}$

None of the above

Correct answer:

$y=9-\frac{x+11}{2}$

Explanation:

Given x=2t-11 and y=-t+9 , let's solve both equations for :

$x=2t-11\rightarrow t=\frac{x+11}{2}$

$y=-t+9\rightarrow t=9-y$

Since both equations equal , let's set them equal to each other and solve for :

$9-y=\frac{x+11}{2}$

$y=9-\frac{x+11}{2}$

Report an Error

Example Question #51 : Parametric

Find $\frac{dy}{dx}$ when $x=t^{2}-5$ and $y=t^{3}-5t^{2}-10t-50$ .

Possible Answers:

$\frac{dy}{dx}=2t$

$\frac{dy}{dx}=\frac{3t^{2}-10t-10}{t^{2}-5}$

$\frac{dy}{dx}=t^{3}-5t^{2}-10t-50$

$\frac{dy}{dx}=\frac{3t^{2}-10t-10}{2t}$

$\frac{dy}{dx}=3t^{2}-10t-10$

Correct answer:

$\frac{dy}{dx}=\frac{3t^{2}-10t-10}{2t}$

Explanation:

If x=x(t) and y=y(t) , then we can use the chain rule to define $\frac{dy}{dx}$ as

$\frac{dy}{dx}=\frac{dy}{dt}/\frac{dx}{dt}$ .

We use the power rules

$\frac{d}{dt}(t^{c})=ct^{c-1}$ and $\frac{d}{dt}(t)=1$ where is a constant, the constant rule

$\frac{d}{dt}(c)=0$ where is a constant, and the additive property of derviatives

$\frac{d}{dt}(a+b)=\frac{d}{dt}(a)+\frac{d}{dt}(b)$ .

In this case

$\frac{dy}{dt}=\frac{d}{dt}(t^{3}-5t^{2}-10t-50)=3t^{2}-10t-10$

and

$\frac{dx}{dt}=\frac{d}{dt}(t^{2}-5)=2t$ ,

therefore

$\frac{dy}{dx}=\frac{dy}{dt}/\frac{dx}{dt}=\frac{3t^{2}-10t-10}{2t}$

Report an Error

Example Question #56 : Parametric, Polar, And Vector

Given x=12-t and y=2t+5 , what is in terms of (rectangular form)?

Possible Answers:

y=29x+2

y=29+2x

None of the above

y=29x-2

y=29-2x

Correct answer:

y=29-2x

Explanation:

Given x=12-t and y=2t+5 , let's solve both equations for :

$x=12-t\rightarrow t=12-x$

$y=2t+5\rightarrow t=\frac{y-5}{2}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-5}{2}=12-x$

y-5=2(12-x)

y=2(12-x)+5

y=24-2x+5

y=29-2x

Report an Error

View Calculus 2 Tutors

Philipp
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mechanical Engineering.

View Calculus 2 Tutors

Andrew
Certified Tutor

Louisiana State University Eunice, Bachelor of Science, Computer Software Engineering.

View Calculus 2 Tutors

Reuben
Certified Tutor

University of Alberta, Bachelor of Science, Mathematics.

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in Philadelphia, SSAT Tutors in Miami, ISEE Tutors in New York City, Biology Tutors in Boston, Reading Tutors in Philadelphia, ISEE Tutors in San Francisco-Bay Area, MCAT Tutors in San Diego, Spanish Tutors in Miami, Algebra Tutors in Miami, Chemistry Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Washington DC, ISEE Courses & Classes in Seattle, ACT Courses & Classes in Denver, GMAT Courses & Classes in Houston, Spanish Courses & Classes in Miami, LSAT Courses & Classes in Denver, Spanish Courses & Classes in Seattle, MCAT Courses & Classes in Philadelphia, ACT Courses & Classes in Boston, MCAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in Seattle, GMAT Test Prep in San Diego, GMAT Test Prep in Houston, LSAT Test Prep in Denver, SAT Test Prep in Washington DC, ACT Test Prep in Denver, ISEE Test Prep in New York City, ISEE Test Prep in San Diego, ACT Test Prep in Boston, SAT Test Prep in Philadelphia

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

Calculus 2 : Parametric Form

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #43 : Parametric, Polar, And Vector

Example Question #561 : Calculus Ii

Example Question #562 : Calculus Ii

Example Question #563 : Calculus Ii

Example Question #51 : Parametric, Polar, And Vector

Example Question #51 : Parametric, Polar, And Vector

Example Question #564 : Calculus Ii

Example Question #52 : Parametric, Polar, And Vector

Example Question #51 : Parametric

Example Question #56 : Parametric, Polar, And Vector

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: