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

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2answers
55 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
150 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
86 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
18 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 ...
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1answer
388 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 ...
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1answer
88 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 ...
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1answer
490 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 ...
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1answer
52 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 ...
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1answer
379 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 ...
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2answers
314 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 ...
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1answer
20 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 ...
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1answer
142 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 ...
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2answers
83 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 ...
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1answer
60 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. ...
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1answer
957 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 ...
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1answer
133 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 ...
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1answer
69 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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189 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 ...
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0answers
43 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 ...
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2answers
79 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 ...
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2answers
106 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
37 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
55 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.
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1answer
2k 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
36 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 ...
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2answers
3k 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 $x=t^2+t$, ...
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1answer
60 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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1answer
821 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
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 ...
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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 ...
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1answer
494 views

Find all points of intersection of the curves $r^2=3\sin(2\theta)$ and $r^2=3\cos(2\theta)$

Find all points of intersection of the curves $r^2=3\sin(2\theta)$ and $r^2=3\cos(2\theta)$. Give your answers as ordered pairs in cartesian coordinates, in order of increasing radius and ...
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0answers
70 views

Beth needs to make a crossing in her canoe

I have a math problem that has me stumped. I cannot seem to find a good starting point for this, and am flying blind with no check values. Maybe it's end of semester fog, but I'm struggling with ...
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1answer
47 views

Paremetric surface revolved around y-axis

if I'm finding the area of the surface generated by revolving the curve around the y-axis I use the equation $2\pi x\sqrt{(x')^2+(y')^2}$ and I'm given $$x=(2/3)t^{3/2}$$ $$y=2\sqrt{2}$$ and I got ...
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48 views

How to define a finite objects with parametric equations

I never had seen parametric equations, but while trying to learn line integrals through Wikipedia, quickly found these equations are remarkable. Some can represent things for which more normal ...
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2answers
137 views

Identifiying the next point on the surface of a cube ( or 3D object )

I have a cube of unit length. Each face of the cube is divided into 10 x 10 equal segments. Consider an object of size equal to that of a segment moving through the surface of the cube ( or any 3D ...
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1answer
19 views

Proving that two function coordinates of a parametric curve equals 1

I am having difficulty with this question, Note: This is not homework, It is from a practice test that I am using to study Consider the curve: $x(t) = \frac{1-t^2}{1+t^2}$ ; $y(t) = ...
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1answer
199 views

Surface Area of a Parametric Curve

Set up an integral that represents the area of the surface obtained by rotating the given curve about the x-axis. Then use your calculator to find the surface area correct to four decimal places. $$ ...
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1answer
64 views

When can I use a parameter in equation (of the a plane)

In my book there is an example: Find vector and parametric equation of the plane $x-y+2z=5$ Now, the solution is: solving for $x$ in terms of $y$ and $z$ yields $x = 5+y-2z$ and then using parameters ...
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2answers
618 views

Finding vector and parametric equations provided only one point.

Normally to answer these questions I have a point and one or two vectors. However, for this one I only have a point. How can I concoct these equations provided there is limited information? Find ...
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1answer
24 views

Finding the velocity vector

Am I finding the equation of the slope of the tangent line at c(t)? $\frac{dy/dt}{dx/dt}$ = $\frac{2t}{3t^2-8}$
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1answer
246 views

Intersection of a parametric curve and a circle

Given a curve defined by a parametric equation $x(t)$ and $y(t)$, how might one calculate the point of intersection with a circle? The derivatives $x'(t)$ and $y'(t)$ are also available if they prove ...
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1answer
48 views

Integration without using parametrization .

I would like to integrate the following line integral without using parametrization . I wanted to integrate the following $$\int_C \frac{1}{z-a} dz$$ , where $C$ is a a curve along $|z-a| =r$ . ...
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2answers
124 views

Parametric Equations: Find $\frac{\mathrm d^2y}{\mathrm dx^2}$.

Find $\dfrac{\mathrm d^2y}{\mathrm dx^2}$, as a function of $t$, for the given the parametric equations: $$\begin{align}x&=3-3\cos(t)\\y&=3+\cos^4(t)\end{align}$$ ...
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1answer
1k views

distance between parametric line and a point (4,3,s)

I've tried solving this problem every way I know how and I just can't get it. I've looked at similar problems of this type, and I still cannot get an answer that seems right. Parametric Equations: ...
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38 views

Can i formulate any curve with parametric equation?

Can i formulate any curve with parametric equation ? if not, so what kind of curves can be explained with parametric equations ?! Thanks in advance
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64 views

symmetric ranges of curve division on an oloid

taken from wikipedia , I drew an Oloid by using the functions with ; ; and with ; ; If I use any equal spaced range of t(x) on ; I will end up with an unequal range t(y), which ...
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1answer
85 views

area under a parametric curve problem

so I have a parametric curve, x = cos(t) y = sin(2t) I found that I need the area from 0 to pi/2. put this into an integral in terms of t I get $$ -\int_0^{\pi/2}sin(2t)sin(t)dt $$ But in my ...
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2answers
105 views

Extend a vector field of normal vectors beyond the surface

I am not terribly well-versed in differential geometry, so please keep that in mind when answering the question. We are given a surface in ${R}^3$ defined parametrically by $\vec{r}(u,v)$ where ...
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349 views

Relation between ellipse general and parametric equation

I am familiar with the fact that one can relate the eigenvectors and corresponding eigenvalues of an ellipse's quadratic equation matrix, to the pose of a circle in 3-space. When say quadratic ...
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1answer
70 views

Determine if a point is contained in the circle in 3d space

I have a problem where I need to determine if a point is contained in the area of a circle in 3d space. For my circle, I have the radius (R), the position of the center (C) and a normal vector to the ...