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Match the parametric equations with the graphs labeled I-VI. Give reasons for your choices. (Do not use a graphing device.)

(a) $ x = t^4 - t + 1 $, $ \; y = t^2 $(b) $ x = t^2 - 2t $, $ \; y = \sqrt{t} $(c) $ x = \sin 2t $, $ \; y = \sin(t + \sin 2t) $(d) $ x = \cos 5t $, $ \; y = \sin 2t $(e) $ x = t + \sin 4t $, $ y = t^2 + \cos 3t $(f) $ x = \dfrac{\sin 2t}{4 + t^2} $, $ \; y = \dfrac{\cos 2t}{4 + t^2} $

(a) Graph V $\\$(b) Graph I$\\$(c) Graph II $\\$(d) Graph VI $\\$(e) Graph IV $\\$(f) Graph III

05:36

Wen Z.

08:46

Bobby B.

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

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So the problem says mass. The parametric equations with the graphs labeled 1-6. Give reasons for the choice is do not use a graphic device. So we are not using graphing device but we know the method for one thing that we can put the equals to zero or infinity. Then we'll see what will be the value of X and Y. Right. So here are few or sanitary equations. Right? So we will see here that what all military equations are there. So this is a solitary right? This is our military. You can say, Okay, I'm sorry. This is 4th 1. Right? So this is arson. It read This is our military. And we can say this is also a solitary. Right? So this is how we find out. Right? So yeah, this is also a signatory. Like so what what can we do now? This is for sure that the part A and B does not contain any sinus or it'll wave or sign costs. I know towns. Right? So it will not have that value. Right? The 2nd, 3rd, 4th and 6th values excluded from it. Right. So now we will solve simply that we can just observe that what is happening in this problem? Yeah. Right. So here we can see this equation parametric equation. Right? Uh, as we put the equals to infinity. Right? So far X and y goes to infinity. Right? If we put equals to infinity here. So X will be infinity and I will be also infinity. So The graph must contain 10 value. Anyone raped. So no. Which is only possible. Which is only possible in cyst because here we can see if we've seen minute lee This is 10 value rate. This is 10. You can see here Here there is 10 coordinated. Right. Can we say this? So the best matches first graph or you can see graph fine. All right. So now moving forward, we can see here X equals two T square minus duty. These this equation is given to us. This is not a solitary. We have already discussed that one and five are not oscillate story. Right? So, we can see here even we can put uh t question infinity as I have told. So, yeah, the equestria infinity. So, this is for sure. After that after conclusion from above. We can also directly right that the answer is one. But we'll see how. So, the equation passes through 00. When we put the equals two in the media. All right. So, this will be 00. Right. So, we are getting the origin. So, best matches. I was thinking bro. What? This is very easy. Yes. No. Now we are moving forward for part C. We can see a people Tequesta by beto then the point should be then point point should be 11 is attained. Right? But it should be it can be minus five to also because the values of uh sine wave varies from minus five to plus five. Two. Yes. So here there could be -1 -1. There would be too cruel conditions. Right so, so here we can see the symmetry here that this is the second graf, right. Second graph if you see keenly the coordinates are 11 year. Right, and here it is, you can see minus one. Oh I'm sorry, this is minus one plus one and this is minus one minus one. We can see here. So that's right option. You can see Graph two is correct. So best matches here, mhm, mhm Drop of doom here, thank you. Now moving forward, we are given with next to equations for X and Y in terms of T. So here We will put equals to zero right at the point when when the equals to zero, then the point should be 10 should be attending. So how could be possible? How could it be possible? It would be possible for graph six white. Because I just see you. Oh 10. It is telling. Right, So here only in draft six, we can see Right here you can see right, this is one zero point. Right, so 10 point is attained in glass sixth. So best matches mhm, graph six, Okay, now moving forward, mm here we are given with value of, you can say the equation for X and Y in terms of T again. So if we put the T infinity. Right, so X and y will also go to infinity but the difference is what? But the difference is one only that it is possible. A Tory in behavior. So let us see you. Okay, so let us compare for E and F. Part. So you Here we'll see 00 cannot be the point in the draft for the Efta part. Right? So whatever is the graph for 00, let us see which one is that? Okay? Mhm. So four? Yeah. Okay. So option you can see Graph four is the answer for this? Best match. Right? Best matches Deborah. Mhm. Now, for the last part we are given with two equations X and Y. Here. Now 00 cannot be the uh tradition. Right? Because here's the scientist is given and this is called given is given. So if one is zero then another should be something is that should be a constant. Right? So it would be constant, not one year rate. So how in which condition it would be possible? So yes, there is no symmetric kind of things that zero and one only exists. So the value is burying in part today. Right. You can see in Graph three, that's why in part we have taken graph four, but not graph three. So best matches here. Rough. Yeah, I hope you understand the concept and this is very easy problem. Thank you for watching. Yeah,

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