Mathematics Stack Exchange
Mathematics Stack Exchange

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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Finding the velocity vector

Am I finding the equation of the slope of the tangent line at c(t)? $\frac{dy/dt}{dx/dt}$ = $\frac{2t}{3t^2-8}$
Quaxton Hale
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Line integral around intersection of sphere and plane

The unit sphere is intersected by the plane $x + y = 14$. Find the line integral of $F = \langle yz + y, xz+5x,xy+2y\rangle$ around the intersection. $$\iint\nabla\times F\cdot\textbf{n}\ dA$$ the unit normal vector is easily found by looking at the…
Benjamin Lindqvist
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Prove parametric equations trochoid

I have to show that the parametric equations of a trochoid are: $x = r\theta - d\sin\theta$ and $y=r-d\cos\theta$ where r is radius and d is the distance between center of the circle and a point P. Can someone please explain this to me? I'm in my…
Sam Creamer
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Question re parametric identity

I am asking whether the existence of a parametric identity involving a set of quadruple signed integers $\{i, j, k, l\}$, which is true for infinitely many sets of quadruples for each integer value of $n, (n>0)$, implies that there is a relationship…
Alex
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Computing tangent and normal for a toroidal helix

I want to align objects on a toroidal helix using the normal and tangent at any point. I have it rendering using the following parametric equations from this post: $$x = (R + r\cos{nt})\cos{t}$$ $$y = (R + r\cos{nt})\sin{t}$$ $$z =…
M-V
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Reverse direction of parametric equation

For the graph $y = \sqrt{x}$ the normal parametric equations would $x = t^2$ and $y = |t|$. However, the direction for that graph would be going from infinity to zero when $t \leq 0$ and zero to infinity when $t \geq 0$. I want that graph to go from…
user88528
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Equation for an asymptotically flat spiral

I would like to find an expression of a spiral which gets straight at infinity, as in the image below: so that I can make a parametric plot.
tupoliedro
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How do I model an oscillation of supply based on producers and consumers?

I'm trying to parametrically model a simple oscillating system representing supply based on production and consumption. The supply should graph something like a sine wave. At any point in time, the change in supply should be equal to production…
Lake
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Parametric Equations rotation of axes

For old coordinates $(x,y)$ the new coordinates $(u,v)$ are related like this: $x = u\cos(\theta) - v\sin(\theta)$ $y = u\sin(\theta) + v\cos(\theta)$ So would it be correct to say that to rotate the axis for a parametric equation defined by $x =…
Cobold
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Parametric curve whose C is part of an equation between two points

So there's this question: Write a parameterized curve whose C is part of the equation $x=y^2-1$ between the points $A=(0,-1)$ and $B=(0,1)$. I've always had some difficulty in parametrizing some equations, but usually ones like this I can easily…
James
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Converting vector form of line in R3 to general form

I have the vector form of a line: $\begin{bmatrix}x\\y\\z\end{bmatrix} = \begin{bmatrix}1\\0\\-2\end{bmatrix} + t\begin{bmatrix}3\\-2\\5\end{bmatrix}$ where $t \in \mathbb{R}$ Normally, to convert a vector equation for a plane in $\mathbb{R}^3$ to…
Joeyboy
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Converting from parametric equation of cube face to general equation

I am trying to convert the vector equation: $\begin{bmatrix}x\\y\\z\end{bmatrix} = \begin{bmatrix}0\\0\\0\end{bmatrix} + s\begin{bmatrix}1\\0\\0\end{bmatrix} + t\begin{bmatrix}0\\0\\1\end{bmatrix}, s,t \in \mathbb{R} $ which represents one of the…
Joeyboy
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Writing a parametric equation in $y=f(x)$ form

I have two equations in $x$ and $y$ in terms of some parameter $t$ as under $$ x(t)=-a.sin(at)-a\ \text{and}\\ y(t)=a.cos(at) .$$ Is it possible to eliminate t and find the relation between $x$ and $y$ in $y=f(x)$ or $f(x,y)=0$?Are there some…
AgnostMystic
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Intersection of a circle and a parametric defined spiral

I am attempting to calculate the intersection of a spiral, defined by the parametric formula $x=\left(t\cdot\cos\left(t\right)\right),\ y=\left(t\cdot\sin\left(t\right)\right)$, and a circle defined as $(x+x_0)^{2}+(y+y_0)^{2}=r^{2}$, where $x_0$…
Tornith
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Parametric equations of a curve (cross section of a tunnel)

I am trying to find out if there is a methodology of finding out the parametric equations of a shape from a picture. To be more specific I am trying to find a way to find x=f(t) and y=f(t) for the picture: Is there any way I can do this by hand? I…
kostaus
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