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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Parametric form of a plane

Can you please explain to me how to get from a nonparametric equation of a plane like this: $$ x_1−2x_2+3x_3=6$$ to a parametric one. In this case the result is supposed to be $$ x_1 = 6-6t-6s$$ $$ x_2 = -3t$$ $$ x_3 = 2s$$ Many thanks.
ocram
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Parametrization for intersection of sphere and plane

Given is the sphere $x^2 + y^2 + z^2 = 4$ and the plane $x + y = 2$ in $\mathbb R^3 $. How can I find a parametrization for the intersection of the two?
user62608
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Do these two parametric equations represent the same curve?

Could anyone help me with this $x = 1 + \cos t$, $y = −2 + \sin t$, $π ≤ t ≤ 2π$; $x = t$, $y = −2 −\sqrt{2t − t^2}$, $0 ≤ t ≤ 2$ For the following parametric equations, how do I determine whether they both represent the same curve? And how to…
ys wong
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Find the point of intersection of the line and surface

I have an odd problem with no solution. I am completely lost on how to solve this. Problem: Find the coordinates of the point(s) of intersection of the line $x = 1+t$, $y = 2+3t$, $z = 1-t$ and the surface $z = x^2 +2y^2$ Attempt: $(1) \ x =…
icelated
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Can (x(t), y(t)) generate a surface? If so, can the surface be continuous?

Intuitively, the parametric equation $z = (x(t), y(t))$ seems to only be able to generate one-dimensional objects, i.e. curves. However... Let $x(t)$ be "the odd-indexed digits of the real number $t$", and let $y(t)$ be "the even-indexed digits of…
user541686
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Investigating the "Wigglyness" of a 2D-Parametric Curve

I am looking to quantify the (for a lack of a better term) "wigglyness" of a parametric curve. The particular set of curves that I am looking at come from cubic-spline interpolation on a set of points that lie, more or less, on a section of a circle…
Jonathan Doucette
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How do you parameterize a circle?

I need some help understanding how to parameterize a circle. Suppose the line integral problem requires you to parameterize the circle, $x^2+y^2=1$. My question is, if I parameterize it, would it just be: $r(t)=($cos $t)i+($sin $t)j$? And how would…
Katie
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Find slope of a curve without calculus

Is it possible to find the slope of a curve at a point without using calculus?
okarin
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Intersection 3D Bézier to sphere parametric

I am coding the intersection of a 3D Bézier curve with parametric equation and a parametric sphere equation, with the objective of splitting the Bézier curve at that specific point. Can you check my equations? I define my sphere and Bézier…
Wilmer Ariza
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Parametric to implicit form of a curve

"Find the implicit form of the curve defined by parametric equations $x = t+1,y=\frac{1}{t^{2}}$" How can I clear $t$ to arrive at the implicit equation?
Nicolás Siplis
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Parametric Curve Representation of a Square from a Circle

Given the parametric equation of a unit circle $$ \vec r(\theta) = \begin{bmatrix} \cos\theta \\ \sin\theta \end{bmatrix}, \quad 0 \leq \theta \leq 2\pi $$ It seems that there is some function $$ f : \mathbb{R} \rightarrow \mathbb{R} $$ such…
Ryan
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Finding parametric and non parametric equations of a plane?

Hi there having some trouble with this. The plane through the three points $(5, 4, -8)$,$(1, 6,-3)$ and $(7,-2,5)$ so I then converted it to $(5, 4, -8) + s(-4, 2, 5) + t(2, -6, 13)$ then converted got $x, y, z$ $x = 5 - 4s +2t$ $y = 4 + 2s -…
James Oliver
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Converting $x=\frac{1}{2}\cos\theta\;;\;\; y=2\sin\theta $ to Cartesian form

How can we transform these parametric equations to Cartesian form? $x=\frac{1}{2} \cos\theta, \quad y=2\sin\theta \quad\text{ for}\;\;0 \leq \theta \leq \pi$
Diego Pacheco
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Equation on parametric form

I'm new to this forum but I've done my best to check that my question hasn't been answered before, but I may have missed something, feel free to correct me if that's the case. Anyway, I'm trying to figure out how to solve this problem: "Determine…
SmhConfused
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Find single parameter value in multi-degree equation to match certain value when all other parameters are locked

Aka there might be a simple name for that question, but here goes: So I'm trying to score objects on certain parameters, one of which is price. The way I calculate the score is I multiply each parameter together. Pretty simple stuff. Ex: score =…
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