00:01
So they want us to show that this parametric curve that we have over here on the left is on this cone.
00:08
And then we're going to use this fact to help us kind of sketch, uh, what we have.
00:13
So the first thing we could do well, let's just kind of put like a little divider down here and then just plug everything in.
00:22
Okay, so we have z's equity, so it's just gonna be t squared.
00:26
Um, then over here on the left.
00:29
So we have x squared.
00:31
So x's t co sign t screw soviet t squared a cosign square t and then why is t scientists that'll be t squared signs square t so let's factor out that t squared so we get t squared times cosine squared plus sine squared teeth.
00:52
And then you might remember that this is just one by pythagoras and so then we get t squared.
01:00
So we have t squared is equal to t squared.
01:01
So we've pretty much shown that this is on the cone.
01:05
So let's go ahead and draw the cone now eso the cone is going toe look, something kind of like this eso kind of goes up like that pretty much all directions and just kind of keeps on our very let me do it this way.
01:23
So i just kind of draw circle if i control a little bit better.
01:30
So the circles she looks something kind of like this little bit smaller down here than it just kind of goes up like that.
01:39
Yeah.
01:40
So this is pretty much what are cone is going toe look like, um, and if i could do a little bit better, it will look more like a comb, so just kind of believe me for right now much.
01:49
Um, but yeah.
01:51
So this is going to be our cone here, and, um oh, actually, i guess the other thing we need, um let me see.
02:01
Do they put a restriction on t? they did not.
02:04
So, actually.
02:05
Well, actually have the other side of this cone also where it's kind of going down.
02:10
Um, so something kind of like this let me try, try a little bit better.
02:22
So something kind of like this and then just going down and yeah, i think that's gonna be pretty much the best i'm gonna be able to do with this count here.
02:33
Um, remember, it'll look like this because z is squared over here so we can plug in positive and negatives and all that.
02:39
Yeah.
02:40
So this is what is gonna look like...