Question
Find parametric equations for the sphere centered at the originand with radius 4. Use theparameters s and t in your answer.x(s,t) = , y(s,t) = , and z(s,t) = ,where ≤ s ≤ and ≤ t ≤ .
Find parametric equations for the sphere centered at the origin and with radius 4. Use the parameters s and t in your answer. x(s,t) = , y(s,t) = , and z(s,t) = , where ≤ s ≤ and ≤ t ≤ .
Answers
Find parametric equations for the sphere $x^{2}+y^{2}+(z-1)^{2}=1.$
Hello? Uh, this problem off to prove that trajectory disposition lives in a circle sphere centered at the origin Some radio sand. If it does, we need to find the radius for two. Two t here for science for the ranging from 0 to 4 pi. What does it mean? That predict relies on? Yeah, uh, straight reporting. So if we're given a corner on, we take one of these. Several of these position say this one. Um, for each position. Victor, we have an initial point 000 at the orange and then in 0.6 was with the Were that I What we want prove use these points for various for burial. Uh, values off our They all lie on a circle, careful around the radio, but circle of fear around the radio, around the origin with radio summaries. It's true that what we need to show that for each of these in points each of these exercises that they satisfy the equation. Wife script. We're equal Griddle radio on. This is the victim. Okay, so we take this as being point on we square them where we had squares green three. If this is some constant square positive number. Then we can take the square root out of it on that would be the radio. So square it's square squaring the nominators four times four squared the same denominator in all three in all three terms So we will use that has come squaring this 16 squaring this use four square on squaring It's 16 far where, uh, see really? Well, take these. We will take for a Terminator have six things We're thinking this term on this but sine squared C But fun group uh, the fundamental Pythagorean this is Well, so you have 16 times oil where we can, uh, fact throughout four from the numerous. And we're like, four. We have proposed squared the denominator. These to cancel Sequels, some squares off. Important old in accordance position. Victor, it's two square. So yes. Therefore, uh, the victory a lot. Uh, you're where radio and that's holders. There you go. Her
So support. We want to start this circle of radius for at the 0.40 So our X coordinate to start off shit before our white corner should be zero. So one possibility we have is to say X is equal to four co sign off T. And then why is he quote to for sign off t. So now, boat for about the X coordinate and the white corn. It will be positive in the first quarter and then they switch signs accordingly. So this center Parametric equations will indeed give us a circle off radius four and it will be traced out the counterclockwise direction to complete the Parametric equations. We just need to say that he goes from 0 to 2 part that will trace out one complete circle.
We consider and circle with the center It could really arching. And the radios iko too far. And this one is Ah, gotta clockwise. So one way, Teoh, formulate the permitted question. Gonna be X equal Jew? No phone Thames course. I'm the d Why we equal Jenna phone time Cy off the tee and the Hagos from the zero to buy. And it wouldn't your craft circle here and we meaning renders it. Could you fall here for on the phone? So I was having a so called It is so indiscriminate. Fall for minus four, minus four here and in goes gotta crack wise here. And this one we can write to stay into the that is in question will be the X squared plus y squared equals Judah for square and coaches six.
So this problem wait can choose X Y SUV we have so far, see, and the competition means for miles you square minds square, uh, has been greater or equal to X squared plus y squared. That means you square plus B square has to relax right with two and we choose a positive branch off the square root, because is Liza Po for corn?