# Tagged Questions

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

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### Moving of 5 units on a curve

If I am at a point (0, 0, 3) and a move of 5 units in the positive direction of $t$ on a curve definite by \begin{align*} x &= 3\sin(t) \\ y &= 4t \\ z &= 3\cos(t)\\ \end{align*} ...
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### Domain and range of locus formed from parametric equations

\begin{cases} x = t^2 + 2t\\ y = 4(t+1)^2 \end{cases} Determine the cartesian equation of the locus? What is the domain of the locus? Note: I have found the cartesian equation: $y=4x+4$ I am just ...
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### Parametrization of a cylinder that is parallel to x axis

The answer is no it does not matter. The surface is $y^2+z^2=4$, I parametrized it so: $\mathbf r=x \mathbf i +2\cos\theta \mathbf j + 2\sin\theta \mathbf k$ But Pauls Outline works through the ...
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### find an appropriate parametrization for the given piecewise-smooth curve in $\mathbb{R^2}$

...for the curve $C$, which goes along the circle of radius $3$, from the point $(3,0)$ to the point $(-3,0)$, and then in a straight line along the $x$-axis back to $(3,0$). So I set the half-circle ...
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### Eliminate the parameter to find a Cartesian equation of the curve.

I got $y=x^\frac{7}{2}$ as the cartesian equation for the following parametric equations, but it is showing up as incorrect. Can anyone explain to me what I did wrong? Thank you!
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### Compute the length of a parametric curve.

It seems like I am not using the good process to compute the length of a given parametric curve. I am not sure if it's inside my calculations or if the steps I use are not correct. The equation of ...
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### Find a parametric representation for an implicit function f(x,y,z)=0

I encountered a very interesting implicit function: $z \exp \left[ (x-0.5-e^{z-y})^2+y^2-0.2z+3 \right] = \sin \left[ (xz-0.5)^2+2xy^2-0.1z \right]$ I wonder if there is any ways to find a ...
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### Length of the curve $\;\;x=3\cos\!\left(6t\right), \;\;y=18t+3\sin\!\left(6t\right), \, \;\; \;\; 0 \le t \le \frac{\pi }{6}\;\;$

The length $\;L\;$ of the curve C given by $\displaystyle \;\;x=3\cos\!\left(6t\right), \;\;y=18t+3\sin\!\left(6t\right), \, \;\; \displaystyle \;\; 0 \le t \le \frac{\pi }{6}\;\;$ is found by ...
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### How to handle this curve? [closed]

I started with differentiation of all three coordinates of this parametrically given curve. I want to show that the respective curve has related equation of the plane and also to prove that it a "...
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### Tangents to Parametrized Curves

I need to find the equation for the line tangent to the curve: $$x = 2\cos t, y = 2\sin t, t = \frac \pi4$$ I also need to find the value of: $$\frac{d^2y}{dx^2}$$ I'm not too sure what to do.. ...
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### Find Cartesian equation from Parametric Equations Including Sec and Tan

Need to find the cartesian equation from: $$x = sec^2t - 1 , y = tan t, -\frac\pi2 \lt t \lt \frac \pi2$$ With sin and cosine I use the unit circle, but I don't know what to do with sec and ...
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### Finding Cartesian Equation giving Parametric Equations

The equations are: $$x = cos(\pi - t), y = sin(\pi - t), 0 \le t \le \pi$$ I don't really understand what to do. On the last problem I had: $$x = cos2t, y = sin2t, 0 \le t \le \pi$$ and I just ...