Mathematics Stack Exchange
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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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How to find t interval in calculating volume of parametric equations rotated

How to find interval $t$ in calculating volume of parametric equations rotated. $$x=2(t-\sin t),~y=2(1-\cos t)$$ Find the volume as curves are rotated around $x$-axis. The interval of $t$ is not given, Is there any way to calculate $t$?
Panda
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Parametric Sweeping of a Rose

My thought process: Create the 2D representation of the rose, which I have defined as : For Domain (u,v) [0,1] x(u,v) = 1 + sin(8π u) cos(2π u) y(u,v) = 1 + sin(8π u) sin(2π u) z(u,v) = 0 May I know how do I manipulate 3π/2 and a vertical…
arc2test
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Proper methods of solving parametric equations

I'm learning parametric equations in this section. Although I understand why the following works, I'm having difficulty understanding why the method employed for solving it is the correct one. I'm instructed to derive a Cartesian equation for the…
Andrew Falanga
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How to eliminate parameter of parametric equations?

If the parameter $t$ of $x$ and $y$ in a plane is given in the interval $(- ∞ , ∞)$ and if $x = t cos (t)$ and $y = t sin (t)$ How can one eliminate the parameter t and write a single equation using only $y$ and $x$?
Amanuel Getachew
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Is it possible to convert the parametric curve defined by $x = t^3 - 3t$ and $y = t^2 - 4$ to an implicit function?

Is it possible to convert the parametric curve defined by $$x = t^3 - 3t \text{ and } y = t^2 - 4$$ to an implicit function?
K. Claesson
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Find the exact length of the parametric curve: $x={e^t}+{e^{-t}}, y=5-2t,0\le t \le 3$.

Find the exact length of the parametric curve: $$x={e^t}+{e^{-t}}, y=5-2t,0\le t \le 3$$ Solution: $$\frac{dx}{dt}=e^t -e^{-t}, \frac{dy}{dt}=-2$$ $$\int_{0}^{3} \sqrt{(e^t-e^{-t})^2+(-2)^2}dt$$ $$= \int_{0}^{3}…
Maggie
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What does it mean by "the consecutive points marked on the curve appear at equal time intervals but not at equal distances"?

What does it mean by the consecutive points marked on the curve appear at equal time intervals but not at equal distances ?
user366312
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how to make parametric equation of cube

this is my hyperbolic equation $y = x^2$ then convert to paramteric equation, like this: $x = u$ $y = u^2$ so i insert the equation into x and y Axis Generator x: u y: u z: 0 the output is: 2D hyperbolic object when i insert v parameter into z…
vaiana
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Find the Cartesian form of the parametric equations: $x=2\sin^2(\theta)$, $y=7\cos^2(\theta)$

I am trying to find the cartesian form of the parametric expressions $x=2\sin^2(\theta)$, $y=7\cos^2(\theta)$. I have $x=2-cos^2(\theta)$ but i can't work it after that.
NeedHelp
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How do I eliminate an element from two parametric equations?

I'm trying to finish some mechanics exercises here but I'm stuck with this, and as I haven't really done math in a while, I can't seem to solve it alone I have two parametric equations: M: $x = e^{3t} + t$ $y = e^{6t} +2e^{3t}t + t^{2}$ Basically…
Edward B
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What is non-parametric equation of a circle?

\begin{align} x & = r\cos t \\ y & = r\sin t \end{align} These are parametric equations of a circle. How can we write an equation which is non-parametric for a circle?
Hamza Erdem
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How do we prove that two parametric equations are drawing the same thing?

For example, if I have $$\begin {align} x(t) &= r\sin t\cos t\\ y(t) &= r\sin^2 t\\ \end {align}$$ and $$\begin {align} x(t) &= \frac r 2 \cos t\\ y(t) &= \frac r 2 (\sin t + 1) \end {align}$$ How do we show that the two parametric equations…
Kang Min Yoo
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Shortest distance between two points moving with the same speed on two lines

I have homework that I have to solve, and the my question is: A cube has side length of 2 cm. One ant starts at corner A and travels to corner B. Another ant starts at corner C and travels to corner D. The two ants leave at the same time and travel…
O-BL
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Convert $x(t)$ and $y(t)$ into Cartesian form

Consider the parametric equations given by \begin{align*} x(t)&=\sin{t}-t,\\ y(t) & = 1-\cos{t}.\end{align*} I want to write these parametric equations in Cartesian form. In order to eliminate the sine and cosine terms I think I probably need to…
user485139
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Reparameterization of ODE

According to some lecture notes for my new course, the following is "easily seen": Let $S$ be a curve parameterized by $\lambda$, so that $S = S (\lambda)$, satisfying $\frac{d^2 S}{d \lambda^2}=0$. Now, changing the parameterization $\xi = \xi…
Henrymerrild
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