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

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1answer
34 views

ratio of tangent to the ellipse

The tangent at point $P = ( a \cos \phi, b \sin \phi)$ on the ellipse $\frac{x^2} {a^2} + \frac{y^2}{b^2}=1$ meets the $x$ and $y$ axes at the points $X$ and $Y$, respectively. Find in terms of ...
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1answer
33 views

Parabolic flight. h(t) vs 2 parametric equations.

Often you have something like: $$h(t)=-16t^2+V_0t+C$$ I have little experience with parametric equations, but I have also seen parabolic functions represented this way: $$x=x_0 + V_{0_x}*t$$ ...
1
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1answer
45 views

How to construct a parametric cubic B spline?

If I am given n+1 control point Pi(xi,yi), Po .... Pn , how do I construct a parametric relationship to draw a curve ? From what I understand , a parametric relationship is that you can express x and ...
1
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1answer
56 views

Express parametric curve as graph of a function

I have a parametric curve in $\mathbb{R}^2$ given by $$ t\mapsto f(t)\left(\begin{array}{c}1\\1\end{array}\right)+\sqrt{-f'(t)}\left(\begin{array}{c}1\\-1\end{array}\right),\quad ...
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0answers
30 views

How are massive parametric functions that make a picture (example inside) created?

[Here's] (http://www.wolframalpha.com/input/?i=sergey+brin+curve) an example of what I'm talking about. The equation might take a second to load. How are these generated, computer algorithms? I ...
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0answers
13 views

Parametric equation from normal line at a certain point

Parametric equation for the normal line -cos4ti + sin4tk, at t = pi/4,I'm working on this problem and truly running into issues. So when I plug in pi/4 I get (-1,0,0), now what? I just don't see how I ...
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1answer
48 views

Asymptote of a parametric equation (with Arctan)

I need to find the asymptotes of a parametric equation. My book says you have a vertical asymptote when $y\to \infty$. But the parametric equation is the following: $$x= \frac 13t^3-\pi,y= \frac ...
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1answer
26 views

Does this limit of arc length exist?

We have a parametrized curve $\gamma: \mathbb{R} \rightarrow \mathbb{R^2}$ given by $\gamma (t) = \langle e^t\cos (t), e^t\sin(t)\rangle$. I want to compute the arc-length of this curve on $[a,b]$ in ...
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2answers
31 views

Eliminate the parameter from the parametric equations

$$x=\frac{3t}{1+t^3} , y=\frac{3t^2}{1+t^3} , t \neq -1,$$ and hence find an ordinary equation in x and y for this curve, The parameter t can be interpreted as the slope of the line joining the ...
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3answers
34 views

Find rectangular equation from parametric equation???

Find rectangular equation from parametric $ x = t^{2} + t $ $ y = t^{2} - t $ I tried finding the equation but I am stuck here: $ x - t^{2} = t $ $ y = t^{2} - t $ $ y = t^{2} - ({x - t^{2}}) ...
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0answers
32 views

How to parametrise this surface integral

This is the question: $ S $ is the boundary of the region $ \{(x,y,z):0≤z≤h, a^2 ≤x^2+y^2 ≤b^2 \}$ where $ h,a,b$ are positive and $a<b$. ${\bf F(r) } = \exp(x^2+y^2){\bf r}$ where $ {\bf ...
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0answers
28 views

Parametric Derivatives

I recently wanted to derive a parametric equation which is as follows: $x(t) = t \cos(\frac{p\pi}{2t})\\ y(t) = t \sin(\frac{p\pi}{2t})$ I derive both equations in terms of $t$ but when I go to ...
1
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1answer
185 views

Finding a vector parametric equation given P and Q equations?

Find a vector parametric equation r⃗ (t) for the line through the points P=(3,5,4) and Q=(1,4,7) for each of the given conditions on the parameter t. If r⃗ (0)=⟨3,5,4⟩ and r⃗ (7)=⟨1,4,7⟩, then r⃗ ...
2
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2answers
98 views

parametrization of plane in $\mathbb R^3$

Parametrize the plane in $\mathbb R^3$ with direction vectors $\hat u$ and $\hat v$ and through the point $p$ as in representation as the range of a $C^1$ function $f:\mathbb R^2\to\mathbb R^3$. ...
0
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1answer
25 views

Can you give a general expression for the rate of rising water poured in an object?

Given an 3-d object defined by a set of parametric equations (x, y, z), can you write a formula expressing the rate that a liquid rises as it's poured into this object at a constant flow rate? Assume ...
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2answers
42 views

Removing parameter $t$ from $z$-axis

How do I remove the parameter $t$ from the $z$-function in the following: $$\begin{align}x&=a\cos{t}-a\\ y&=a\sin{t}\\ z&=nt\end{align}$$ (where $n,a$ are arbitrary coefficients) So far I ...
3
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2answers
156 views

Arc length paramatrizations satisfy original system of differential equations?

Say we have a system of differential equations $$ \begin{cases} x'''(t)+f(t)x'(t)=0\\ y'''(t)+f(t)y'(t)=0 \end{cases} $$ on an interval $[a,b]$, along with the restriction that $$ x'(t)^2+y'(t)^2=1 $$ ...
0
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1answer
51 views

How can I increase the resolution of a 3d plot in Sage to see all the details of the noodle? [closed]

I want to plot my noodle with a high resolution to see all the details. How can I achieve this with Sage? Here is my parametric, piecewise function: ...
2
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3answers
70 views

Parametrization of $y^2 - x^2=1$

I have found parametrizations for the level curve $y^2-x^2=1$, however, I have a question regarding one of them. From the Pythagorean trigonometric identity $\cos^2 x + \sin^2 x =1$ we obtain ...
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2answers
42 views

Find a parametrization of the intersection curve between surfaces

Find a parametrization of the intersection curve between the surfaces $−3x^2+2z=10$ and $4x^2+10y^2=5$. You should parametrize such that $y=k\sin(t)$ for some constant k. The answer should be in ...
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1answer
80 views

Gradient of a rational Bezier curve

I'd appreciate help working out the gradient of a rational Bezier curve $C = (\,x(t) \,, \,C_y(t) \,)$. I know that the gradient $g$ of a the parametric curve is $$ g(t) = \left( \frac{dy(t)}{dt} ...
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1answer
66 views

Find the shaded areas A1, A2, A3

I think i know how to find the angles KAG and KAH that's what i did: (this is the picture from my assignment sheet) then i have to find the shades areas A1,A2 and A3 but i don't know how to ...
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0answers
17 views

Derivative of a parametrized vector on a nonfixed basis

Suppose a curve defined by a vector parametrized through the variable $u$, and expressed on a non-fixed base, like the polar coordinates base. You derive it with respect to that parameter. What ...
1
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1answer
98 views

Coordinate of intersection between line and square

TL;DR given a square and a point $p$, I need the intersection between the perimeter of the square and a ray cast from the center of the square through point $p$. This is my approach so far, but I will ...
1
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1answer
70 views

sketch the line segment whose parametric equations

Sketch the line segment whose parametric equations are $x=2+t, v=t^2-1, t∈[0,3]$ That's what i did $t=x-2$ $v=(x-2)^2-1$ $v=x^2-4x+3 $ $v=(x-3)(x-1)$ $x=3,1$ and that's my sketch I am not ...
0
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1answer
74 views

Find a vector equation and parametric equations or the line in R^3 that passes through the point (1,2,-3) and is parallel to the vector u=(4,-5,1).

Find a vector equation and parametric equations or the line in $\mathbb{R}^3$ that passes through the point $(1,2,-3)$ and is parallel to the vector $u=(4,-5,1)$. Find two points on the line that are ...
2
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1answer
42 views

Quick Parameterization Help

I've been trying to paramaterize $$x^2+y^2+z^2=9,\ x^2-y^2=3$$ but haven't had any luck. I was thinking to let $x=\sqrt{3}\ \sec(t), y=\sqrt{3}\ \tan(t)$ to complete the identity on the right ...
0
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1answer
85 views

Find a vector equation and parametric equations of the line in $\mathbb{R}^2$ passing through the origin and is parallel to the vector $\vec{u}=(2,3)$

anyone can help me? :< Are there any equations that I could use in this question? I am so confused. I only know how to do the question if it changes "parallel" to "perpendicular" because I only ...
0
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0answers
56 views

Parametric equations and specifications of a triskelion (triple spiral)

I haven't been able to find the parametric equations and specifications to form a triskelion, a triple spiral (this is made of three interlocked couples of spirals). Using the parametric equation of ...
0
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1answer
14 views

Parametrizing curve with not only one peak

I obtained experimental data (thermal analysis) and need to parametrize the resulted curves for modeling. An example of two curves obtained: I tried to use a Weibull distribution, but since I ...
1
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1answer
90 views

Circle On Sphere

Sorry if this sounds too silly but my math skills are very poor and I just need this problem fixed. I made this graphic with geogebra 3D and it was quite easy there but I don't know how to write ...
2
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2answers
60 views

When does this parametric curve cross itself?

Find the points where the curve given parametrically by$$\mathbf{r}(t)=\left(2+\cos\frac{3}{2}t\right)\left(\begin{matrix}\cos t\\\sin t\end{matrix}\right)$$crosses itself. So, I understand that ...
2
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1answer
44 views

There exists a constant arc length parametrization

I heard that for any curve in the plane that can be given parametrically by $\vec{r}(t)=\langle x(t),y(t)\rangle$ for $a\leq t\leq b$ that there exists a constant arc length parametrization, i.e. ...
0
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1answer
167 views

Understanding the Equation of a Möbius Strip

I am in HL Math and trying to finish my IA. My topic is the Möbius band. The only problem is, I do not understand the formula that defines it and everywhere I have looked has just given me a ...
1
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1answer
88 views

Tangent Line of a Parametric Curve

Deduce the equation of the tangent line to the curve defined by the equations x=cosh(t), y=sinh(t), and z=ct I have somewhat of a good grip on the definition of a ...
2
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1answer
59 views

Find slope of a curve without calculus

Is it possible to find the slope of a curve at a point without using calculus?
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0answers
71 views

What is the parametric and cartesian equation of a hyperbolic paraboloid formed by the intersection of two cylinders of radius “A” & “B”?

What is the parametric and cartesian equation of a hyperbolic paraboloid formed by the intersection of two cylinders of radius "A" & "B", which intersect at a distance of "H" from its Axis at an ...
1
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0answers
33 views

Line integral, Parametrization

I have this line $A=\{(x,y) \in R^2 : y^2+4x^4-4x^2=0\}$ , $(x>0)$ I parametrized it like that : $b(t) = (t, \sqrt{4t^2- 4t^4})$. And my $F$ is $F(x,y) = (x+y,-x)$. But when I calculate my ...
2
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2answers
47 views

Searching for a probability distribution appropriate for my task

I'm making a game (not important), but I'd like to have real probability distribution function (instead of classical dice notation). I like the normal distribution, but I would like to also shift the ...
0
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2answers
80 views

Cartesian equation of $ \vec{r}(t)=\left(e^{\omega t}(\cos(\omega t)+\sin(\omega t)),2\omega e^{\omega t} \cos(\omega t)\right) $

I have this parametric equation: $$ \vec{r}(t)=\left(e^{\omega t}(\cos(\omega t)+\sin(\omega t)),2\omega e^{\omega t} \cos(\omega t)\right) $$ and I have to obtain the Cartesian equation. Any ...
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1answer
32 views

can the derivative of a closed complex contour at any point be zero?

If C is a closed contour in the complex plane parametrized by z(t)=u(t)+i*v(t), can there be any point where z'(t)=0?
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1answer
52 views

Parametrize $|x|+|y|+|z|=1$

How can we parametrize the surface $|x|+|y|+|z|=1$? Here I mean differentiable parametrize. I think we may need to divide it into 8 pieces and consider them respectively.
1
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1answer
540 views

find parametric equations for the path a particle that moves along the circle $x^2+(y-1)^2=4$

Find parametric equations for the path a particle that moves along the circle $$x^2+(y-1)^2=4.$$ In the manner describe a) One around clockwise starting at $(2,1)$ b) Three times around ...
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2answers
32 views

Show that the parametric equation $ x=x_1+(x_2-x_1)t , y=y_1+(y_2-y_1)t$

Can anyone help me to solve this? Show that the parametric equation $ x=x_1+(x_2-x_1)t $ $ y=y_1+(y_2-y_1)t\ $ with $(0\le t\le 1)$ describe the segment that joint the point $P_1=(x_1,y_1)$ and ...
0
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2answers
778 views

how to convert this parametric equation into a Cartesian equation.

I did not know how to answer this question Sketch the curve by using the parametric equation to plot points. indicate with arrow the direction in which the curve is traced as t increases $x=t^2+t$, ...
1
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1answer
51 views

Finding the length of a parametric curve

$$x=\frac{t^2}{2} \text{ , } y=\frac{(2t+1)^{3/2}}{3} \text{ , } 0 \le t \le 20$$ The formula for the length of a parametric curve is $L=\int_{a}^{b}\sqrt{[f'(t)]^2+[g'(t)]^2}dt$. Taking the ...
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votes
1answer
142 views

Find Equation of a Perpendicular Line Going Through a Point

I have the following parametric equation for line g: $$ x=3t\land y=-7+5t\land z=2+2t $$ I have to find the equation of a line perpendicular to $g$ and going through point $Q(3,-2,4)$ which lies on ...
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1answer
54 views

Write $y=\cos x -7$ in parametric equation [closed]

How do I write $y= \cos x-7$ in a parametric equation? I'm not sure how to do this.
0
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1answer
51 views

Direction of t (Vector Space)

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. $$x = e^{-t}\cos t, y = e^{-t} \sin t, z = e^{-t}; (1, 0, 1). $$ The ...
2
votes
1answer
56 views

Area of a band in $\mathbb{R}^2$

If I have a continuous, and smooth curve $\mathcal{C}$, length $\ell$, in $\mathbb{R}^2$ and at each point on the curve I were to draw a line segment, length $d$, normal to the curve centered at the ...