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Questions tagged [parametric]

For questions about parametric equations, their application, equivalence to other equation types and definition.

In mathematics, a parametric equation of a curve is a representation of this curve through equations expressing the coordinates of the points of the curve as functions of a variable called a parameter. This contrasts with implicit equations that define a curve as the zero set of some equation in the coordinates.

The parametric forms of curves are well-suited for drawing on a computer, while their corresponding implicit forms are useful for analytic manipulations (intersections, etc.)

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Parametric equations - stating values.

A curve is defined by the parametric equations: $x=\cos2t, y=\sin2t, 0
James786
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What's the equation of this parametric surface?

disclaimer: my math is sketchy at best AND english is not my first language, so... i might have some issues naming things - but i'll try my best to be clear :) given this parametric curve: see it on wolfram alpha. anyway, its equation is (sorry if…
fffact
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Intersection of two parametric lines

This is not a question on my homework, just one from the book I'm trying to figure out. They want me to find the intersection of these two lines: \begin{align} L_1:x=4t+2,y=3,z=-t+1,\\ L_2:x=2s+2,y=2s+3,z=s+1. \end{align} But they do not provide any…
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Give the explicit form of the following parametrized surface

Let $\boldsymbol{X}:\boldsymbol{R}^2\to \boldsymbol{R}^3$ be the paramtrized surface given by$$\boldsymbol{X}(s,t)=(s^2-t^2,s+t,s^2+3t)$$ I'm trying to describe the parametrized surface by an equation of the form $z=f(x,y)$
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Parametric form of curves?

Can someone tell me the steps to get the parametric form of a curve? For example: $x^{2\over 3}$ +$y^{2\over 3}$ =1
user128576
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Parametric equations where sin(t) and cos(t) must be rational

Suppose there are parametric equations $$ x(t) = at - h\sin(t) $$ $$ y(t) = a - h\cos(t) $$ and it is required that both $\sin(t)$ and $\cos(t)$ should be rational. What the values of $t$ should be in that case? Thanks.
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Quick Parameterization Help

I've been trying to paramaterize $$x^2+y^2+z^2=9,\ x^2-y^2=3$$ but haven't had any luck. I was thinking to let $x=\sqrt{3}\ \sec(t), y=\sqrt{3}\ \tan(t)$ to complete the identity on the right equation, but when going back to the left one and…
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Parametric Equations (Basic) - Cartesian equation of curves

$x = 2 \cos t$, $y = 2 \sin t$, $0 \le t \le 2\pi$ Find the Cartesian equation of the curves. Please help i know it's basic but my problem is that $2 \cos t$ doesn't equal $1 - \sin^2 t$ and if it does how? (maybe i just need a re-freshener). Help…
MATHSUSER
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Is there a way to plot this graph into a helical shape in three dimensions?

This is a continuation of my question from Physics, Is there an equation representing the movement of a longitudinal wave?. It is referring to this animation. I don't know much about notations on longitudinal waves, but here is my modification…
soupless
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Finding the coordinates of a point of intersection from a pair of parametric equations.

A curve is given by: $$x = 2t + 3 $$ $$y = t^3 - 4t$$ The point $A$ has parameter $t = -1$. Line l is a tangent to the curve at $A$. Line l cuts the curve at point $B$. Find the value of $t$ at $B$. I've worked out that the equation for l is: $2y +…
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Parametric equation for plane with $\langle 0,1,1\rangle + s.\langle 1,0,-1\rangle$ and $\langle 0,0,-3\rangle + t.\langle 2,1,2\rangle$

In $3$-dimensional space, two lines $l_1$ and $l_2$ are given parametrically as follows: $$ X = \langle 0,1,1\rangle + s.\langle 1,0,-1\rangle \text{ and } Y=\langle 0,0,-3\rangle + t.\langle 2,1,2\rangle $$ How would you write the parametric…
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How to interpret this task?

I have a task given to me in my homework I can not figure out what asks of me. The task is worded like this: A curve in a plane is given by $$ x(t) = 3(t - \sin(t)) $$ $$ y(t) = 3(1 - \cos(t)) $$ Find the parametric normal-curve $x(s, t), y(s, t)$…
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Parametric formulas for ray cast question

I apologize if the question is elementary, I am having problems understanding if what I am doing is correct. Write parametric formulas $x(u), y(u) $for the ray cast from the point with coordinates $(1, 2)$ through the point with coordinates $(4,…
arc2test
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How to find intercept between a line and a parametric equation with exponentials?

I have the following equations: Eq. 1) A standard equation for a line $$y=mx + b,$$ Eq 2) A a parametric equation $$x=e^{at}-1,$$ $$y=e^{ct}-1,$$ where $a$ and $c$ are known constants. I want to find the intercepts of Eq .1 with Eq. 2.In the…
bart cubrich
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How do I show the full solution for this?

My lecturer gave us a potential bonus to the grade if we can fully solve those equations: $y^x=9 $ $x^y=8$ easy to see that the value of $x$ and $y$ are $2$ & $3$ but what is the correct full way of showing the solution for that? appreciate your…
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