Parametric Curves - Basic Graphing

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! * IN MY FIRST EXAMPLE, THERE IS A 'SMALL' MISTAKE. INSTEAD OF GRAPHING t ON THE INTERVAL [0,5] I ACTUALLY USE [0,4]. SORRY FOR ANY CONFUSION!!*
Parametric Curves - Basic Graphing. In this video, I discuss some of the very basics about graphing parametric curves. One example of eliminating the parameter is shown.
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[@dopeybears737]

Are you in pre cal and understand how to find curve with a table, if so reply ASAP!! I have a couple equations

[@fahinrahman8951]

@@dopeybears737 I just finished calc 2, I had to review this from before but I'm not sure what I can help with

[@dopeybears737]

Fahin Rahman I’m in pre cal, i have a table filled with numbers, and if need to write a set of parametric equations, I’ll make a short utube vid of the question if u can help

[@dopeybears737]

Fahin Rahman i just uploaded, a video, it’s a pass or fail if i get a good grade on this assignment, if u would like to comment how to solve it in the comments of my help vid that would be great

[@patrickjmt]

no problem! lots of comments. you did remind me to add some annotations though, so thanks again! i do not leaving mistakes unrecognized!

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im taking the SAT 2 in math tomorrow.. and i never learned this before, this definitely helped... thanks!

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[@verky56]

Wait these type of problems are in calc 3? I’m doing this for precalc.

[@TheFadedBanana]

@@verky56 I've taken pre-calc, calc 1, calc 2, ODEs, and Linear Algebra, and I havent done anything with parametrics until calc 3. You've got bad luck lol

[@patrickjmt]

no problem - happy to help

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Wow, this video was 10 years old a couple of days ago. Imagine all the people it's helped in that time!

[@patrickjmt]

just do a substitution like i do at the end of the video to get y = x^2 in your example

[@patrickjmt]

ya, matador pointed it out! i will add annotations now : ) thanks again!

[@patrickjmt]

@tbair200 glad you like my stuff :)

[@patrickjmt]

well, one reason they are used is so that you can describe curves in the plane that are not functions!

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@metalmine1 perhaps if universities valued teaching that would be true...

[@WhatElseExceptNature]

Thanks a lot Patrick! You really helped me with this video, something my calculus AP teacher failed to do - tons of help! :) I feel 90% prepared for my test tommorow now.

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[@WHY70122]

My prof teaches us to get rid of t before graphing and i find that way is so much harder. Thanks to you, life gets way easier. This is my 3rd semester learning math without a freaking text book :))

[@thenateman27]

No, because the graph of the parametric curve is based off of x=root(t). Negative t values would result in imaginary numbers. In Eliminating the parameter, he squared the root(t), but the implied domain of "t is greater than or equal to 0" still remains. So really, the cartesian version exactly is y=1-x^2 where x is greater than or equal to 0. Hope this helps

[@patrickjmt]

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[@patrickjmt]

@Kaanzzzz ha : ) good luck in your studies!

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thank you that seriously helped so much i didnt understand these at all but now i get the basics thank you

[@amedeo24]

@jaibhambra no, its because of your domain. x = sqrt(t) so you can't plug in a negative because it will result in an imaginary number

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[@patrickjmt]

it would be t = 4 since x = 1 + (4)^1/2 = 1+2=3

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somehow i doubt that...

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[@patrickjmt]

ops, i see what you are saying, i think i messed up! thanks matador!

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[@Nuhjeea]

Sorry I just realized what you said in the description, correcting this error. It may help a tiny bit to also have an annotation pop up during the video saying "This should be t = 5 and NOT t = 4"

[@joeympower]

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[@vishula1]

Wasn't it t=4, and it's not terminal point? Because 0

[@LemuelUhuru]

Yeah, I believe the terminal point is at (root(5),5). Edit: Checkout the description he changed the interval from [0,5] to [0,4]

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[@1SmartTouch]

Hey Patrick ,thank you so much for this helpful tutorial the other thing is there was a hard question in my book ,, that was like this . they put a graph of X with respect to T ,and they put a graph of Y with respect to T ,, they want me to predict how the graph of Y with respect to X ,, I would really appreciate it if make a video about how to solve such problems : ]

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[@Nuhjeea]

at about 4:00 , Patrick states that t=5 is the terminal point. I see why that is since it is given but do we not need to graph the terminal point like we did with the starting point?

[@bluekate123]

Around 3:20: why do you take the positive root of 4 and ignore the negative value?? (-2)^2 is also equal to 4.

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Thanks a million patrickJMT

[@patrickjmt]

@razorchallhan hahah, no enemies that i want destroyed.... yet. ; ) the best thing, better than any donation, is to spread the word and recommend the videos to your friends. or just tell random people on the street if you want.

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for a problem like x=sin(t) & y=csc(t) 0

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[@karnabudhathoki5311]

My understanding about graphs of curve is.....you have to have the understanding about the nature of them...unlike graphs of straight lines you cannot plug in x and y values by brute calculation....so you need to understand the nature...e.g graph of parabola is y= ax^2. if a is positive the graph is curved upwards and if a is negative the graph is curved downwards...also the value of a has correlation with the width of parabola.....and of course...graphing calculators and computers can graph curves well...but we as people have to have understanding of the curve natures...

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[@rug963]

Yay, this is making sense now

[@Alejo1916]

In the 2nd question the domain of t was (-infinity to +infinity)... can t take negative values?

[@hahachobo]

haha the first example you used was the first question in my textbook!

[@dangkhanhlinh476]

Yes. this is exactly what i need. thanks

[@danielw9542]

does the intervals of t have to be 1 or are the intervals based on however accurate you want your graph to be?

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[@LilFrisk3232]

wait so doing the Tchart method, is every coordinate you get on the graph?

[@Supermario0727]

Does this mean that you can define a curve using vector equations?

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@patrickJMT You got it, man

[@ShinyJewels04]

i have a question.. i have a problem where negative infinity < t < positive infinity, and x = 3t and y = 9t^2. please help! i don't understand

[@tantrumgrunt]

Nice video! You must know alotttt of calculus :D! But one question, what if they don't give you an interval for the parametric equations?

[@horsesandacorns2503]

u saved my life

[@ShinyJewels04]

ok thanks, but i still don't understand how to graph it? which t values should i start with and how many should i plug in? i know there are no initial or terminal points, but it's asking me to graph it and then indicate the direction that the curve is traced.. if t had bounds i would be ok but because t doesn't, i'm so confused

[@kambojk]

Wait so, if there are no restrictions on the parameter in the second example, why does the initial point start at (0,1)? Is that just for the values you chose?

[@joshuatrumanmaxwell4004]

I'm probably way too late, but I believe it's because of the domain restriction of the square root of t

[@Richarez]

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[@jaibhambra]

when he put t=4, how comes he didn't take the x value to be equal to -1? do you only use the positive root?

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[@eternity23211]

if given the picture for the curve, how do you find the parametric equation?

[@benjaminparkin9716]

Kalvin Wong I think the only way is to find 2 parametric equations which give a shape that matches the graph. IE guess

[@rockingk3853]

What if there is no restriction to 't' then how would we graph it? just choose any values for 't'?

[@way7952]

Hey if you get back around to this video could you put in an annotation for the note you made in the comments? Thanks.

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