# Tagged Questions

The parametric tag has no wiki summary.

4answers
185 views

### Parametrization for intersection of sphere and plane

Given is the sphere $x^2 + y^2 + z^2 = 4$ and the plane $x + y = 2$ in $\mathbb R^3$. How can I find a parametrization for the intersection of the two?
1answer
148 views

### How are the parametric equations describing the cupid curve derived? [duplicate]

No doubt as some people have already seen, today morning wolfram posted the best valentine ever. The graph depicting cupid with its arrow and floating hearts around it involves something like 6 pages ...
1answer
212 views

### Converting parametric equation to implicit form

So I have the equation defined in homogeneous coordinates $[w; x, y]$ as $[1+t^2; 1-t^2, 2t]$ $$w = 1+t^2$$ $$x = 1-t^2$$ $$y = 2t$$ If I do $w+x-y$ I get $-2t+2$, so $t = -(w+x-y-2)/2$. I was then ...
2answers
34 views

### Parameterized curve describing trajectory of thrown object

We describe the trajectory of a thrown object (neglecting friction and similiar effects) with the curve $$k(t) = \left(v_0\cos(\beta)t,\,v_0\sin(\beta)t-\frac{g}{2}t^2\right)$$ with ...
1answer
66 views

### Domain of parametric equation

If there is a parametric equation $x=2\cos{2t}$ and $y=6\sin{t}$, $0\le t \le \frac{\pi}{2}$ the Cartesian equation is $y=3\sqrt{2-x}$. How do I find the domain of the Cartesian equation? I tried: ...
2answers
116 views

### Plotting parametric equations in gnuplot

I am trying to plot the following parametric equation in gnuplot: fx(t) = -35*cos(t) + 65*cos(-.35*t) ...
0answers
176 views

### Parametrization of square to calculate Dot-product in line-integrals and area-integrals, electric field from $\frac{dB}{dt}$?

I am calculating 3A of Tfy-0.1064 in Aalto University. I realized here that I am misunderstanding something in vector calculus: the thing market in green particularly. I know \nabla\times E= ...
1answer
92 views

### equation for the region inside a circle

What equation or group of equations fill the entire or part of a region inside a circle without using inequalities? Update I don't know if this problem is already solved, I'm trying to find the ...
2answers
110 views

### Understanding cubic bezier curve

I do not have experience of Mathematics past a-level, so please excuse the incorrect terminology. I am trying to better understand the fundamentals of how a cubic bezier curve works. I am going by ...
2answers
34 views

### what's the algebra (if any) behind converting f(x) for a circle to a parametric equation

I'm sure there has to be some algebra behind it. My problem called to covert $$(x - 2)^2 + (y - 9)^2 = 4$$ if $x = 2 + 2cos(t)$ then $y = ?$ I know the answer is $9 + 2\sin(t)$ but I simply got ...
2answers
107 views

### parametric curves, parameter and integration

I just started learning about parametric curves and I find it confusing that we have a 3rd variable but this 3rd variable "t" is some imaginary variable....I dont get what the difference is between ...
3answers
267 views

### Writing Polar Equations In Parametric Form

For an example problem, in my textbook, the author wanted to demonstrate how to graph a polar function. Deeming it most convenient, my author took the polar function $r=2\cos 3\theta$, and re-wrote it ...
1answer
62 views

### Parametric Equation of a Circle Using a Line

Consider the unit circle $$x^2+y^2=1.$$ How can I parametrize it using the line $y=m(x+1)$, where $m$ is its slope?
1answer
59 views

### Help me understand a surface integral question?

The question is: Evaluate the surface integral: $$\iint\limits_S \, x^2yz\ \mathrm{d} S$$ Where S is part of the plane z = 1 + 2x + 3y that lies above the rectangle [0,3] X [0,2] I literally just ...
1answer
88 views

### Finding parametric equations

I am trying to understand volume and surface integrals. I do get the idea of the process (find a parametric equation of the volume/surface, integrate afterwards). But I just cannot make up parametric ...
0answers
79 views

### Finding parametric equations

I am trying to understand volume and surface integrals. I do get the idea of the process (find a parametric equation of the volume/surface, integrate afterwards). But I just cannot make up parametric ...
1answer
82 views

### Find the Frenet frame

Consider the following space curve: $$\gamma(x)=(e^x\cos(x), e^x\sin(x), e^x).$$ My main goal is to find the Frenet Frame T,N,B. So far I have found the arc-length using the following formula:  ...
2answers
145 views

### Converting $x=\frac{1}{2}\cos\theta\;;\;\; y=2\sin\theta$ to Cartesian form

How can we transform these parametric equations to Cartesian form? $x=\frac{1}{2} \cos\theta, \quad y=2\sin\theta \quad\text{ for}\;\;0 \leq \theta \leq \pi$
2answers
55 views

### Converting $x = \sin \frac{t}{2}, y = \cos \frac{t}{2}$ to Cartesian form

How can we transform these parametric equations to Cartesian form? $$x = \sin \frac{t}{2}, \quad y = \cos \frac{t}{2}, \quad -\pi \leq t \leq \pi.$$
3answers
70 views

### Help me to sketch this parametric curves

Is there any defined process to sketch parametric curves? Thanks in advance. $$x = \cos^2 t, \quad y = 1 - \sin t, \quad 0 \leq t \leq 2\pi.$$
1answer
47 views

### Find a function f(x) such that the parametric curve could be obtained by flipping the graph

Find a function f(x) such that the parametric curve could be obtained by flipping the graph of f across the line with slope 1 that goes through the origin. parametric curve with coordinates (t^14, ...
3answers
109 views

### 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) ...
1answer
115 views

### Arc Length Of Parametric Curve

I attached the problem as a file: Where did the trig functions go? I sifted through the different trig identities and formulas, but couldn't find anything that I could use. What should I do?
2answers
595 views

### Finding Where A Parametric Curve Intersects Itself

The problem I am working on is to find the where the curve intersects itself, using the parametric equations. These are: $x=t^2-t$ and $y=t^3-3t-1$ For the graph to intersect itself, there must be ...
1answer
665 views

### Finding Where A Parametric Curve Crosses Itself

The parametric functions I am dealing with are: $x=2\sin2t$ and $y=3\sin t$ I know for a parametric graph to cross itself, there must be two distinct $t$, $t_1$ and $t_2$, that when placed into the ...
1answer
196 views

### Finding Parametric Equations For A Rectangular Equation

I am trying to find a general way of finding parametric equations for a rectangular equation. The problem I am working on is $y=x^3$, and I have to find two examples of parametric equations. ...
2answers
99 views

### Parametric Equation Problem

The problem is, "to determine any differences between the curves of the parametric equations. Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain." (a) \$x=t;\quad ...
1answer
62 views

### Restriction Of Parametric Functions Domain

The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the ...
2answers
31 views

### Need help with this parametric equation

$s(t)=(\frac{2}{t^2+1},\frac{2t}{t^2+1})$ I need to calculate a line integral along this path. But I have trouble understanding what it is. I did some googling and it looks that it is a parabola, but ...
2answers
37 views

### How do I find the 2 slopes at which this parametric function crosses itself?

I have a parametric function. If you graph it, you'll find that it looks like a figure 8. x(t) = 2sin(2t) y(t) = 8sin(t) How do I find the slopes of the function ...
1answer
251 views

### Parametric equation of a cone

I usually use the following parametric equation to find the surface area of a regular cone $z=\sqrt{x^2+y^2}$: $$x=r\cos\theta$$ $$y=r\sin\theta$$ $$z=r$$ And make $0\leq r \leq 2\pi$, \$0 \leq \theta ...
0answers
63 views

### complex circular motion

Assume the planet orbits its star in a circular orbit of 100 units with period 360 days. The moon in turn orbits its planet at a radius of 10 units and period 28 days. Finally the moon rotating, we ...
1answer
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### Can (x(t), y(t)) generate a surface? If so, can the surface be continuous?

Intuitively, the parametric equation $z = (x(t), y(t))$ seems to only be able to generate one-dimensional objects, i.e. curves. However... Let $x(t)$ be "the odd-indexed digits of the real number ...
2answers
86 views

### Parameter values that make function values side lengths of a triangle

I have been trying to solve the following problem for more than a week without any success. Given the function: $$f(x)=\frac{x^2+mx+4}{x^2+x+4}$$ Find all possible values of the parameter $m$ such ...
1answer
55 views

### How can I re-write an equation (or system of equations) in parametric form?

For the equation $y = 3x$ I need to re-write $x$ and $y$ in terms of a variable $t$. How can I find the value of each variable in terms of $t$?
1answer
73 views

### How to find a parametric equation?

I want to find an equation for a race track, so I could get the position of a point with respect to time. Let's say I have this track and here are a few points on it: Could it be possible to model ...
1answer
56 views

### parametrizing quarter of a circle

I am given the circle whose equation is: $(x-\frac{1}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{1}{2}$. So, the coordinates of the origin of the circle are: $(\frac{1}{2},-\frac{1}{2})$ and the radius of the ...
1answer
141 views

### converting a parametric R5 vector into a Cartesian form

How do you solve a problem like this. I'm completely stumped. it seems like there should be an easy solution but I'm obviously over looking it. any help would be greatly appreciated.
2answers
78 views

### Constant velocity of a sine function

I am defining the location of an object based on the sine function. The position of the object at s seconds along the x-axis is defined as x=s and its position along the y-axis is defined as y=sin(x). ...
1answer
221 views

### Find the area bounded by the parametric curve…

Find the area bounded by the parametric curve $x = \cos(t)$, $y = e^t, 0 < t < \pi/2$, and the lines $y = 1$ and $x = 0$. I do not even know where to start with this problem. I know that I need ...
3answers
1k views

### How to find a parametric equation for the tangent line to the curve of intersection of the cylinders?

How can i find a parametric equation for the tangent line to the curve of intersection of the cylinders $x^2 + y^2 = 4$ and and $x^2 + z^2 = 1$ at the point $P_0(1,\sqrt{3}, 0)$?
1answer
78 views

### How do we find the length of the line (parametric curve)?

A curve in the $xy$-plane is given parametrically by $$x(t) = e^{2t}, \quad y(t) = e^{2t} \sin(2t), \quad t \in [0, \pi/2].$$ What is the length of this curve? Ok, actually I know what to do, ...
1answer
61 views

### Converting parametric equations in a numerical equation

Is it possible convert this parametric equations in a numerical equation? $$\begin{cases} \displaystyle x(t)=tv_0\cos(\theta)\\ \displaystyle y(t)=tv_0\sin(\theta)-\frac{1}{2}gt^2+h \end{cases}$$ ...
0answers
41 views

### Maximum value for parameter

I am facing the following problem: A number of a adults, b children older than 12, and c children younger than twelve attend an event. The sum of all people a+b+c=100. The prices are \\$6 per adult, ...
1answer
783 views

### Equation for making a circle in 3D space

I have a 3D space with axis $(x, y ,z)$ and I can make a circle in the $xy$-plane. To make a circle in the xy-plane I currently use spherical coordinates $(r, \theta, \phi)$ where $r = 1$, \$\theta = ...
1answer
207 views

### Parameterize a straight line using polar coordinates… without angle.

I had to parameterize a straight line with starting point in $A=(-3,7)\\$ and endpoint in $B=(4,1)$. My idea was to use the equation for the line that goes through two points. That is:  \frac { ...
1answer
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### Parametric Equation of a Particle Movement inside a Vortex in a Rectangular Box

I am trying to simulate the movement of a particle in a vortex in a rectangular box, I am currently using an ellipse but that causes the particle to collide with the walls more that I want. The ...
2answers
101 views

### Finding Tangent line from Parametric

I need to find an equation of the tangent line to the curve $x=5+t^2-t$, $y=t^2+5$ at the point $(5,6)$. Setting $x=5$ and $y = 6$ and solving for $t$ gives me $t=0,1,-1$. I know I have to do ...
1answer
376 views

### Parametric Equation

Let $P_1$ be the plane through the origin containing the vectors $[1,2,-1]$ and $[0,1,1]$. Let $P_2$ be the plane through the point $(1,1,1)$ parallel to the vectors $[-1,2,2]$ and $[3,4,-2]$ I know ...
1answer
31 views

### Represent sorting position by a parametric form

Given a set of random integers {0,5,100,65,...,0,1,2}, is there a mathematical method existing to construct a parametric form $f$ (the number of parameters $<<$ the number of integers) so that ...
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