# Tagged Questions

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

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### Parametric Equation part A

Hi everyone I am in need of some guidance solving this parametric equation question and was wondering if you guys could give me some pointers and to see if I am doing this correctly. Here I have two ...
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### Name this 2-dim Parametric Curve

is there a name for the following parametric curve? Thanks. I encountered it when playing around with the tangent lines and normal lines of an ellipse. The parameter $\theta$ is the same parametric ...
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### For which values of t does a matrix not have eigenvalues

I need help solving this problem "For which values of real parameter t does the matrix: \begin{bmatrix} π^2t^2 & 36\\ -36 & 0 \\ \end{bmatrix} NOT have real eigenvalues. Thank you.
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### How to graph hypocycloid on graphical calculator

I want to know how I can graph a hypocycloid using my TI-nspire calculator. I already know the parametric equations for hypocycloids which is: Parametric Equations of Hypocycloids Does anyone know ...
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### Hypocycloid with an outer ellipse

I have tried to change the traditional hypocycloid a bit. What I've basically done is that a circle now rolls inside an ellipse. I am trying to find the equation for the same. I am mostly done, ...
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### Solving the following parametric equation

Solve the following parametric equation: $$\frac{-(3\cos t-x)}{2\sin t-y}=-\frac{2\cos t}{3\sin t}$$ So I need to find the parametric equation of the thing in terms of $t$. But I am confused ...
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### Cycloids with ellipse

I have been researching about the epitrochoids and hypotrocoids lately. I was wondering if it would be possible for us to have an ellipse rolling around a circle? If so, then how could one derive its ...
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### How to find a Bezier curve without control points?

Let's say someone created a cubic Bezier curve using software and rasterised it. However, the original equation of the Bezier curve was not noted. Since we have the image of the Bezier curve, we can ...
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### Why isn't the gradient vector of a parametric curve parallel to the tangent vector?

Consider a parametric curve defined by the equation: $$\mathbf{r}(t) = X(t)\mathbf{\hat{i}} + Y(t)\mathbf{\hat{j}} + Z(t)\mathbf{\hat{k}}$$ Paul's online math notes indicate that the unit tangent ...
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### straight to helix transition

I am trying to get cylindrical parametric equations for a straight line to helix transition, where the straight line is the centre axis of the helix. From what I can deduce, a straight line is a helix ...
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### Finding area of hypocycloids (without integration)

I have been trying to find the area of hypocycloids, I understand how to do it with integration. But the thing is I wanna find some other method for finding its area. In one of the sites online, I ...
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### Another method of finding area of hypocycloids

I was finding the are the of hypocycloids. Then it struck me that apart from integration, there could be another method of finding the area of the hypocycloid with different curves. But the problem is ...
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### Help writing a parametric equation from this complex polar one

A particle is moving along the curve $r=4-2\sin(\theta)$ at the moment when $\theta = t^2$. I need to write a x(t) and y(t) function that will model the particle behavior with its x position and y ...
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### Hi, I have been trying to understand the derivation of a hypocycloid's parametric equation, but am stuck with one part.

I have been using someone else's answer on the same site to understand the problem: here's the link - Parametric equations for hypocycloid and epicycloid I can understand everything but the part ...
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### Determine the largest area of an ellipse enclosed by the hyperbolas ($xy=1$ and $xy=-1$)

Question: An elipse with equation $${x^2\over a^2} + {y^2\over b^2} = 1$$ is enclosed by the hyperbolas given by $xy=1$ and $xy=-1$. , Determine the largest area of an ellipse enclosed by the ...
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### cycloid of a unit-speed circle

In one of the lectures of the MIT OCW Multivariable Calculus course, the professor introduces the parametric equation of a cycloid in the plane, where $a$ is the radius of the circle that creates it, ...
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### Baricenter of a region bounded by a parametric curve

I just want to ask if there exists a general rule to get the baricenter of a region bounded by a parametric curve?
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### Find the limit of the vector function

$lim_{t\to\infty} \Big(te^{-t},\frac{t^3+t}{2t^3-1},tsin(\frac{1}{t})\Big)$ a) $lim_{t\to\infty} te^{-t} = \infty \times 0$ $lim_{t\to\infty} 1e^{-t}+-e^tt = 0+(0\times\infty)$=undefined, and ...
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### Curve of intersection, value for parameter

This is for a line integral. Parametrize the curve of intersection: \begin{align*} S_1: x^2+4y^2 + z^2 &= 4a^2, y<0\\ S_2: x+2y &= 0 \end{align*} Orientation from $(0,0,-2a)$ to $(0,0,2a)$....
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### Find an equation tangent to the curve at the point corresponding to the given value of the parameter

$x = 1 +4t -t^2$, $y = 2 - t^3$, at $t=1$ $\frac{dy}{dx}$ $= \frac{-3}{2}$ at t = 1. Where do I go from here?
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### Paramerization for compact rational knots of degree 6?

The algorithm computes but it computes rational function of degree 8. I am interested in rational knotted functions of degree 6. Perhaps relevant publications here on non-compact curves of degree 6 ...
### Eliminate the parameter given $x = \tan^{2}\theta$ and $y=\sec\theta$
$x = \tan^{2} (\theta)$ and $y = \sec (\theta)$ knowing that $\tan^{2} (\theta) = (\tan (\theta))^2 = \dfrac{\sin^{2}\theta}{\cos^{2}\theta}$ and that $\sec(\theta) = \dfrac{1}{\cos(\theta)}$ $\to$ ...