Parametric equation of a parabola rotating on its axisGive the equation of the surfaceThe $y$ coordinate when rotating around the $x$-axis.Surface area of lateral section of paraboloidEquation of a coneWrite the parametric equation of the revolution surface generated by the line when it rotates around the axis $Oz$.Convert Surface of Revolution to Parametric EquationsRotating a conic section to form a 3d shapeEquation of a parabola, given the vertex and the axisParametric Equations of an Ellipsoidal HelixParametric equations for the surface of revolution generated by rotating the hyperbola $z^2−y^2=2$ about the $y$-axis
Is "history" a male-biased word ("his+story")?
What is the dot in “1.2.4."
Why must traveling waves have the same amplitude to form a standing wave?
Potentiometer like component
Want to switch to tankless, but can I use my existing wiring?
Does splitting a potentially monolithic application into several smaller ones help prevent bugs?
The meaning of the "at the of"
Should QA ask requirements to developers?
Sword in the Stone story where the sword was held in place by electromagnets
When were linguistics departments first established
Is it illegal in Germany to take sick leave if you caused your own illness with food?
Single word request: Harming the benefactor
Decoding assembly instructions in a Game Boy disassembler
How to deal with a cynical class?
Running a subshell from the middle of the current command
Plywood subfloor won't screw down in a trailer home
Silly Sally's Movie
How could a female member of a species produce eggs unto death?
Best mythical creature to use as livestock?
Welcoming 2019 Pi day: How to draw the letter π?
Word for a person who has no opinion about whether god exists
Making a sword in the stone, in a medieval world without magic
Ban on all campaign finance?
"One can do his homework in the library"
Parametric equation of a parabola rotating on its axis
Give the equation of the surfaceThe $y$ coordinate when rotating around the $x$-axis.Surface area of lateral section of paraboloidEquation of a coneWrite the parametric equation of the revolution surface generated by the line when it rotates around the axis $Oz$.Convert Surface of Revolution to Parametric EquationsRotating a conic section to form a 3d shapeEquation of a parabola, given the vertex and the axisParametric Equations of an Ellipsoidal HelixParametric equations for the surface of revolution generated by rotating the hyperbola $z^2−y^2=2$ about the $y$-axis
$begingroup$
Write the parametric equation of the surface generated by a parabola
rotating around its axis.
I guess it's simply getting from the parabola equation to the parametric equations of a generic paraboloid. But I don't know how to get to the param. equations of that surface of revolution.
Any help would be really appreciated.
geometry surfaces
asked Mar 10 at 20:03
Mandelbrot Jr.Mandelbrot Jr.
175
$endgroup$
add a comment |
$begingroup$
Write the parametric equation of the surface generated by a parabola
rotating around its axis.
I guess it's simply getting from the parabola equation to the parametric equations of a generic paraboloid. But I don't know how to get to the param. equations of that surface of revolution.
Any help would be really appreciated.
geometry surfaces
asked Mar 10 at 20:03
Mandelbrot Jr.Mandelbrot Jr.
175
$endgroup$
add a comment |
$begingroup$
Write the parametric equation of the surface generated by a parabola
rotating around its axis.
I guess it's simply getting from the parabola equation to the parametric equations of a generic paraboloid. But I don't know how to get to the param. equations of that surface of revolution.
Any help would be really appreciated.
geometry surfaces
asked Mar 10 at 20:03
Mandelbrot Jr.Mandelbrot Jr.
175
$endgroup$
Write the parametric equation of the surface generated by a parabola
rotating around its axis.
I guess it's simply getting from the parabola equation to the parametric equations of a generic paraboloid. But I don't know how to get to the param. equations of that surface of revolution.
Any help would be really appreciated.
geometry surfaces
geometry surfaces
asked Mar 10 at 20:03
Mandelbrot Jr.Mandelbrot Jr.
175
asked Mar 10 at 20:03
Mandelbrot Jr.Mandelbrot Jr.
175
asked Mar 10 at 20:03
Mandelbrot Jr.Mandelbrot Jr.
175
asked Mar 10 at 20:03
Mandelbrot Jr.Mandelbrot Jr.
175
asked Mar 10 at 20:03
Mandelbrot Jr.Mandelbrot Jr.
175
175
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Like in other cases where the former $x$ axis becomes a rotating axis, it is natural to swith from $x$ to $r$ and to name the fixed vertical axis $z$ in replacement of $y$, i.e., transform $y=x^2$ into $y=r^2$ i.e., finally :
$$z=x^2+y^2tag1$$
which is the cartesian equation of the paraboloid.
If you want parametric equations from (1), just take :
$$(x,y,z)=(x,y,x^2+y^2)tag2$$
but if one prefers to take polar coordinates in the horizontal plane $x=r cos theta, y=r sin theta$, we obtain another parametric set of equations :
$$(x,y,z)=(r cos theta, r sin theta, r^2)tag3$$
answered Mar 10 at 20:50
Jean MarieJean Marie
30.7k42154
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3142822%2fparametric-equation-of-a-parabola-rotating-on-its-axis%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Like in other cases where the former $x$ axis becomes a rotating axis, it is natural to swith from $x$ to $r$ and to name the fixed vertical axis $z$ in replacement of $y$, i.e., transform $y=x^2$ into $y=r^2$ i.e., finally :
$$z=x^2+y^2tag1$$
which is the cartesian equation of the paraboloid.
If you want parametric equations from (1), just take :
$$(x,y,z)=(x,y,x^2+y^2)tag2$$
but if one prefers to take polar coordinates in the horizontal plane $x=r cos theta, y=r sin theta$, we obtain another parametric set of equations :
$$(x,y,z)=(r cos theta, r sin theta, r^2)tag3$$
answered Mar 10 at 20:50
Jean MarieJean Marie
30.7k42154
$endgroup$
add a comment |
$begingroup$
Like in other cases where the former $x$ axis becomes a rotating axis, it is natural to swith from $x$ to $r$ and to name the fixed vertical axis $z$ in replacement of $y$, i.e., transform $y=x^2$ into $y=r^2$ i.e., finally :
$$z=x^2+y^2tag1$$
which is the cartesian equation of the paraboloid.
If you want parametric equations from (1), just take :
$$(x,y,z)=(x,y,x^2+y^2)tag2$$
but if one prefers to take polar coordinates in the horizontal plane $x=r cos theta, y=r sin theta$, we obtain another parametric set of equations :
$$(x,y,z)=(r cos theta, r sin theta, r^2)tag3$$
answered Mar 10 at 20:50
Jean MarieJean Marie
30.7k42154
$endgroup$
add a comment |
$begingroup$
Like in other cases where the former $x$ axis becomes a rotating axis, it is natural to swith from $x$ to $r$ and to name the fixed vertical axis $z$ in replacement of $y$, i.e., transform $y=x^2$ into $y=r^2$ i.e., finally :
$$z=x^2+y^2tag1$$
which is the cartesian equation of the paraboloid.
If you want parametric equations from (1), just take :
$$(x,y,z)=(x,y,x^2+y^2)tag2$$
but if one prefers to take polar coordinates in the horizontal plane $x=r cos theta, y=r sin theta$, we obtain another parametric set of equations :
$$(x,y,z)=(r cos theta, r sin theta, r^2)tag3$$
answered Mar 10 at 20:50
Jean MarieJean Marie
30.7k42154
$endgroup$
Like in other cases where the former $x$ axis becomes a rotating axis, it is natural to swith from $x$ to $r$ and to name the fixed vertical axis $z$ in replacement of $y$, i.e., transform $y=x^2$ into $y=r^2$ i.e., finally :
$$z=x^2+y^2tag1$$
which is the cartesian equation of the paraboloid.
If you want parametric equations from (1), just take :
$$(x,y,z)=(x,y,x^2+y^2)tag2$$
but if one prefers to take polar coordinates in the horizontal plane $x=r cos theta, y=r sin theta$, we obtain another parametric set of equations :
$$(x,y,z)=(r cos theta, r sin theta, r^2)tag3$$
answered Mar 10 at 20:50
Jean MarieJean Marie
30.7k42154
edited Mar 10 at 20:59
answered Mar 10 at 20:50
Jean MarieJean Marie
30.7k42154
answered Mar 10 at 20:50
Jean MarieJean Marie
30.7k42154
answered Mar 10 at 20:50
Jean MarieJean Marie
30.7k42154
30.7k42154
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3142822%2fparametric-equation-of-a-parabola-rotating-on-its-axis%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
