## anonymous 5 years ago The parametric representation r(s,t)=2tcos(s)i + 2tsin(s)j + tk for s∈R and t∈R corresponds to what surface? What is mean by s∈R and t∈R?

1. anonymous

R means the set of all real numbers.

2. anonymous

i see, thanks. For this question, is it starts with x=2tcos(s), y=2tsin(s),z=t? what are the next steps?

3. anonymous

i see, thanks. For this question, is it starts with x=2tcos(s), y=2tsin(s),z=t? what are the next steps?

4. anonymous

give me a minute

5. anonymous

ok.$t=z \implies x^2+y^2+z^2=5z^2 \implies x^2+y^2=$. your aim is to find a relationship between x,y and z, and get rid of all the parameters.. $x ^{2}+y ^{2}+z ^{2}=4t^2+\cos^2t+4t^2\sin^2t+t^2=4t^2(\cos^2t+\sin^2t)+t^2$ that's$x^2+y^2+z^2=5t^2$ , but t=z, $z=t \implies x^2+y^2+z^2=5z^2 \implies x^2+y^2=4z^2$

6. anonymous

$x^2+y^2=4z^2$ is cone ,, so the parametric equations are correspondent to a circular cone

7. anonymous

The selections of answer are as below: a)$4z^{2}=x ^{2}+y^{2}$ b) $2x + 2y + z = 5$ c) $z = 4 y ^{2}$ d) $x ^{2} + y ^{?} = 4$ e) $4z ^{2} = x ^{2} + y ^{2}$ Why are u using x ^{2}+y^{2}\] + z2 = $5z^{2}?$ how we know it is$5z^{2}?$

8. anonymous

The selections of answer are as below: a)$4z^{2}=x ^{2}+y^{2}$ b) $2x + 2y + z = 5$ c) $z = 4 y ^{2}$ d) $x ^{2} + y ^{?} = 4$ e) $4z ^{2} = x ^{2} + y ^{2}$ Why are u using x ^{2}+y^{2}\] + z2 = $5z^{2}?$ how we know it is$5z^{2}?$