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

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2answers
33 views

Need help to understand a math task about algebraic and parametric equations

Can anybody please explain this for me?: Find the algebraic and parametric equations of the circle with centre (-2,3) that passes through (1,-1) How do I find the algebraic and parametric ...
0
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1answer
19 views

Parametric to Cartesian equation conversion [on hold]

Need to convert this parametric equation to Cartesian equation. $$x=\sec(t)\quad y=\tan(t) \\ -\frac{\pi}{2} < t < \frac{\pi}{2}$$
0
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1answer
27 views

Parametric curve parametriced by length

Normally you have a parametric curve with a variable t and you increment t to find the point along the curve. Is it possible to have a curve so that given a value it will give you the point on that ...
0
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0answers
22 views

Parametric vector form of cartesian equation

Cartestian equation: $$-2x-y+z=6$$ I know to find the parametric vector form we can find any 3 points P, Q and R which satisfy the cartesian equation. $$ \begin{pmatrix} x_1\\ y_1\\ z_1 ...
0
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1answer
16 views

Identifying self-intersection points in one parametric graph.

My question for you is how to identify self-intersection points in a parametric curve of the form x = f(t), y = g(t). The specific problem asks for the t values of the intersection where $x = ...
1
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1answer
772 views

Find 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 a vector equation and parametric equation of 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 ...
0
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1answer
28 views

Parametric Equation explanation

Explain how the expression $tX + (1-t)Y$, $0\le t\le 1$, produces a segment that connects point $X (x_1, y_1)$ with point $Y (x_2,y_2)$. So I rearranged the problem such that $t(X - Y) + Y$ which I ...
1
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1answer
17 views

Paramaterization of paraboloid and plane.

Consider the paraboloid $z=x^2+y^2$. The plane $2x-4y+z-6=0$ cuts the paraboloid, its intersection being a curve. Find "the natural" parameterization of this curve. I have set each equation equal ...
1
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1answer
28 views

Using L'Hospital's Rule on Parametrics [on hold]

Stuck on this problem... Let C be the curve given by the parametric equations $x = f(t)$, $y = g(t)$ and let $$\left(f\left(t_0\right), g\left(t_0\right)\right)$$ be a point on the curve. Let $m(t)$ ...
-3
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0answers
25 views

Parametrize the given curve. [closed]

$x^2 + y^2 = 121\;$ satisfying the condition $\;\displaystyle c(0) = \left(\frac{11}2, \frac{11\sqrt{3}}2\right)$ Thank you! 
1
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8answers
120 views

How can I parametrize $|x|+|y|=1$

I need parametrize $|x|+|y|=1$ but I don't know how to parametrize. I know that it is a rotated square, I would like understand so if you can explain to me like if I was still, thanks
0
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1answer
2k views

Find a parameterization for the circle of radius 2 in the xy-plane, centered at the origin, clockwise

Find a parameterization for the circle of radius $2$ in the $xy$-plane, centered at the origin, clockwise. I know to use $2\cos(t)$ and $-2\sin(t)$ but I'm not sure what to do after that
3
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1answer
31 views

How do I represent a Mobius Band Triangle Parametrically

I am trying to describe a Mobius band in the shape of a triangle like this: parametrically in terms of its $x$, $y$, and $z$ functions. Is this even possible? I know a basic mobius strip can be ...
1
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2answers
31 views

Convert between parameteric ellipse equations

I have the parametric equation of an ellipse in this form: $$x(t)= a\cos(t)$$ $$y(t)=b\cos(t+\phi)$$ It's an ellipse centred about the origin, with a tilt angle. So three parameters. How can I ...
2
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1answer
35 views

Conditions that guarantee a composite Bezier curve in the cartesian plane represents a function?

Context I am allowing users of my application to control a curve connecting $(0,0)$ and $(1,1)$. There are a finite number of knots that are evenly spaced horizontally. The user can specify the ...
1
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0answers
35 views

Intersection between a parametric equation and a linear equation

2Consider the parametric functions $f_1, f_2$ with $$f_1(x) = 3(60-x)\cdot \sin(3x)$$ and $$ f_2(x) = 3(60-x)\cdot \cos(3x).$$ Suppose you have a linear function: $$f_3 (x) = 1.5 x$$ How does one ...
0
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2answers
28 views

How can I know whether the airplanes collide by using parametric equations

Recall that a line hes equation y=mx+c. Suppose one airplane moves along the line y=2x+3 while the other airplane moves along the line y=3x-2. By plotting a graph, even though the lines are intersect, ...
1
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1answer
111 views

Converting between explicit function and parametric function

Given an explicit function $y = f(x)$, how to convert it to the respective parametric functions $x = f_1(t)\; y = f_2(t)$? Given parametric functions $x = f_1(t)\; y = f_2(t)$, how to obtain the ...
0
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1answer
11 views

How to parametrise a parabola with a specific domain

What would be the best method to find the parametric equations for the parabola $y = (x-2)^2$ over a given domain of $(2 ≤ t ≤ 5)$? The figure I've been given has the parabola starting from $(2,0)$ ...
7
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2answers
2k 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 ...
2
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2answers
436 views

Equation of a parabola in 3D space

I have two points with coordinates A(x1,y1,z1) and B(x2,y2,z2). There is a third point which is vertex(lowest point) of the parabola. I only know z-coordinate of this point. I need to find coordinates ...
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1answer
22 views

How many solutions depending on the parameter (augmented matrix?)

I have to find how many solutions have got the following equations, depending on p parameter? $ \begin{bmatrix} 5 & p & 5 \\ 1 & 1 & 1 \\ p & p & 2 \end{bmatrix} $ $ ...
0
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2answers
304 views

Line integral around intersection of sphere and plane

The unit sphere is intersected by the plane x + y = 1. Find the line integral of F = around the intersection. $\int\int\nabla$x$F\cdot$ n dA the unit normal vector is easily found by looking at the ...
0
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1answer
1k views

Parametrization for the curve $y = 7 - x^4$ that passes through the point $(0, 7, -3) $when t = 0 and is parallel to the xy-plane

Can you help me? So far I have turned $y = 7-x^4$ into $\langle1, 1, 0\rangle$ and used it to make the equation $L = (0, 7, -3) + t(1, 1, 0)$. I know this is wrong, but I just don't know what, and I ...
0
votes
2answers
30 views

Differentiate the parametric function and find $dy/dx$ and $d^2y/dx^2$

Differentiate the parametric function and find $\frac{\mathrm dy}{\mathrm dx}$ and $\frac{\mathrm d^2y}{\mathrm dx^2}$ in terms of "$t$" when: $ x = \frac{1}{t-1}$ and $y = \frac{1}{t+1}$ I have ...
4
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2answers
67 views

Investigating the “Wigglyness” of a 2D-Parametric Curve

I am looking to quantify the (for a lack of a better term) "wigglyness" of a parametric curve. The particular set of curves that I am looking at come from cubic-spline interpolation on a set of points ...
1
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2answers
38 views

Showing that the image of a curve lies on a surface?

I am looking for an intuitive explanation to a problem in one of my practice tests. I'm given a parameterized curve from $\Bbb R$ to $\Bbb R^3$, called ${\bf r}(t) = (\sin t \cos t, \cos^2 t, \cos ...
2
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2answers
2k 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 $r⃗ (7)=(1,4,7)$, ...
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2answers
23 views

Parametric equations: Finding the ordinary equation in $x$ and $y$ by eliminating the parameter from parametric equations

I am having difficult time solving the following equation: Eliminate the parameter from the parametric equations: $x=\frac{3t}{1+t3}$ and $y = \frac{3t^2}{1+t3}$ where $t \ne−1$ and hence find an ...
45
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5answers
3k views

Do “Parabolic Trigonometric Functions” exist?

The parametric equation $$\begin{align*} x(t) &= \cos t\\ y(t) &= \sin t \end{align*}$$ traces the unit circle centered at the origin ($x^2+y^2=1$). Similarly, $$\begin{align*} x(t) ...
1
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1answer
27 views

Parametrizing motion of string around rod

I'm trying to solve this problem with calculus. A string is wound symmetrically around a circular rod. The string goes exactly 4 times around the rod. The circumference of the rod is 4 cm. and its ...
1
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0answers
13 views

parsimonious definition of a zig-zag function between two bounds

Suppose I have some strictly increasing function $f:[0,b]\to[0,b]$ with $0<b<1$, $f(x)<x$ and $f'(b)=\frac{1-f(b)}{1-b}$ (i.e. tangent to the secant line to $(1,1)$). Now imagine a 'tunnel' ...
1
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1answer
65 views

Locus of solution of an ODE system

I have an ODE system $$ \ddot p = \frac{ p \left( {2p - 4} \right) }{{p - 4}}{{\dot q }^2 } \\ \ddot q = \frac{{3p - 8}}{{p - 4}}\dot q \dot p $$ Short of finding closed-form expressions for ...
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1answer
32 views

Line integral of a vector field? [closed]

First of all, sorry for the sketch.. I would be glad if you show me another ways to improve this drawn. I'm studying Line integrals, and this question is really boring me. Please, can someone put ...
0
votes
2answers
292 views

Is this valid parametric equation to create control points for a helix in 3D space?

Is this a valid way to compute new points that are on a helix and if not what is it wrong? The Cartesian coordinates of each new helix control point could be described by the following ...
0
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1answer
21 views

Parabola Question - simultaneous equations?

I'm having trouble with the second part of this question. I can do the first part by finding the normal at P and where it intercepts with U and then for the second part i've substituted each point ...
1
vote
2answers
17 views

Use the discriminant to show that $mx−y + m^2 = 0$ touches the parabola $x^2 =−4y$, for all values of m.

Use the discriminant to show that $mx−y + m^2 = 0$ touches the parabola $x^2 =−4y$, for all values of m. I attempted to solve by letting them both equal each other, but it didn't work. How do I do ...
1
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1answer
348 views

Parameterizing an ellipse

Given the ellipse $(x-1)^2 + \frac{y^2}{4}= 1$, parametrize the curve in polar coordinates. I've forgotten something very basic here. Can someone help get me started?
1
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2answers
19 views

Find, in terms of $s$,the coordinates of the point where this normal cuts the curve again.

a) Find the equation of the normal at the point $(2s,\frac{2}{s})$ to the curve whose parametric equations are $x=2s,y=\frac{2}{s}$ b) Find, in terms of $s$,the coordinates of the point where ...
2
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2answers
36 views

Gradient vector of parametric curve

I have ellipse $$(\frac{x}{a})^2 + (\frac{y}{b})^2 = 1$$ Gradient is $$(\frac{2x}{a^2}, \frac{2y}{b^2})$$ How I can obtain this vector from parametrization of my curve? Let I know only $$(x, y) = (a ...
1
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2answers
30 views

Radius of a wheel based on parametric equations

I am working on a question and I don't have the slightest idea where to begin. Any nudge in the right direction would be very helpful. Here is the question: A bicycle wheel has radius R. Let P be ...
4
votes
4answers
41 views

Eliminate $t$ to give an equation that relates $x$ and $y$

I am having problems understanding how to solve the following parametric equation. I have achieved an answer, but am unsure if my answer is correct or not. Eliminate t to give an equation that ...
0
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1answer
17 views

If PQis a focal chord, show that the interval RU is parallel to the axis of the parabola.

For part (c) of question thirteen am I only required to find the gradient of RU and prove that is it zero? This is how I have interpreted this question. ANY help on the matter is much appreciated ...
1
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1answer
28 views

Parametric Curve Tangent Equations

Let a curve be given in the parametrized form by: $r(t) = (2\cos t, 2\sin t), 0 \leq t \leq 2\pi$ Find the equations of the tangents to the curve at each of its points $(X_0, Y_0)$. Having gone ...
1
vote
2answers
32 views

How to parametrise $x^2 + y^2 = z^2; z \in [0, 1]$?

How to parametrise $x^2 + y^2 = z^2; z \in [0, 1]$? I want to parametrise so I can use the divergence theorem to calculate the flux along the surface above. I don't know how to do it and would like ...
0
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1answer
24 views

Is there a method to parameterise any surface? And how could I parametrise this one given?

I'm having major trouble every time I need to parametrise a surface in order to take a surface integral, I just have no idea where to even start half of the time. Is there some kind of method that can ...
8
votes
0answers
96 views

Is “imposing” one function onto another ever used in mathematics?

First of all, let me define what I mean by "imposing." Basically, I mean graphing some function with respect to some other function, rather than with respect to the x-axis. To be more specific, for ...
2
votes
0answers
35 views

Tweaking Reddit's Ranking Algorithm

This image explains how Reddit's Ranking algorithm works. As you know, Reddit is a very high traffic site. Therefore, the post rank decreases quite fast. This algorithm puts emphasis on bringing ...
2
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3answers
45 views

Find the coordinates of the point where the normal cuts the curve again problem

Find the equation of the normal to the curve $x=2\cos\theta$, $y=3\sin\theta$ at the point where $\theta=\frac{1}{4}\pi$. Find the coordinates of the point where this normal cuts the curve again. ...
0
votes
2answers
20 views

To find a extremal point of a function with parameters

I have a function $$f(x) = (x-5m)(x+m)^2$$ I have tried to find the extremal points of this function (and then find if it's local maxima or minima). That means I need to find the x of derivative. The ...