# Tagged Questions

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

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### Maximum Height is giving me negative

Hey guys for this parametric equations its giving me negative Question is: A dart is thrown from a point 5 feet above the ground with an inital velocity of 58 ft/sec and angle of elvation of 41∘. ...
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### Parametric Problem: Throwing a Dart <Test Review>

Yup it's me ... Parametrics, who would have thought xD! Anyways, again ... I am doing review and I really need this grade to get an A in math class; that's why I am asking questions here. And you guys ...
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### Parametric Problem: Kicking a football (Getting Ready For Test)

As I told you on title I'm getting ready for a test. I have this Test-Review Problem.... A football is kicked from the ground with an initial velocity of $28$ ft/sec at an angle of $28^\circ$. How ...
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### How to fit a set of 3D points to a helical curve?

suppose I have a set of points in $\mathbb{R}^3$, and I want to find an arbitrary helix which best approximates these points. An arbitrary helix in $\mathbb{R}^3$ can be parametrized as ...
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### Intersection of a smooth plane curve and a circle

Let $\gamma(t)=(x(t),y(t)):[0,2\pi] \rightarrow \mathbb{C}$ be a $C^1$-Jordan curve. How to show that there is a small circle $C$ that intersects $\gamma$ only at two points?
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### Gradient function of a circle

The parametric equations of a circle $C$ are: \begin{align*} x&=2+\dfrac{13}{5\sqrt{2}}\cos t\\ y&=1+\dfrac{13}{5\sqrt{2}}\sin t \end{align*} for $t\in[0,2\pi]$. I am stuck on this part: Find ...
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### Parametric Problem

i have a question on parametric.. The question states A vector equation $(x,y) = (2,-1) + t(3,2)$. Write as a parametric equation. Show a table with x,y values. Sketch a picture of vector ...
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### 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 ...
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### Parametric Equations Problem

Im back! Um, i have a simple question im trying to get ready for test after 5 days.. I slacked of sadly :( on math, so i have to pick up my skills.. On my test review i have this question: The ...
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### How can I find the necessary speed and speed of rotation for a problem from a parametric equation?

I have been given the following questions for a project that I am currently working on: Questions 1 to 8 I have completed questions 1 through 6 but have no idea how to do questions 6 or 7 after ...
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### Heuristics for putting $f(x_0,x_1,\ldots,x_n)=0$ into parametric form?

Suppose I have an implicit equation: $$f(x_0,x_1,\ldots,x_n)=0$$ Which might be 'paramaterizable'; i.e. put it into the form: \begin{align} x_0 &= ...
In this question: Find the area bounded by: $x=\ln(t)$, $y=\frac{t-3}{t-1}$, $3\leq x \leq 5$, and by the $x$-axis (it is above the $x$ axis). I solved the integration parametric curve, $3\ln(t) ... 2answers 2k views ### Parametrization for the curve on cylinder$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)$. I know this is wrong, but I just don't know what, and I ... 1answer 35 views ### How do parametric equations work? I was given a graph like this in my exam. Its defined para-metrically by x=c^2 and y =c^3. It won't help me now but could someone explain this to me why I have two seemingly different lines I know ... 1answer 25 views ### Finding minimum plus maximum of$g(a)=\int_{0}^{\pi/2} |\sin 2x-a\cos x|dx$Let $$g(a)=\int_{0}^{\pi/2} |\sin 2x-a\cos x|dx,\quad a\in[0,1].$$ If$L$and$M$are the minimum and maximum values of$g(a)$for all$a\in [0,1]$. Find the value of$L+M$. The first thing ... 1answer 26 views ### Paramteric Curves and the exponents of$\cos$/$\sin$/$\tan$Lets say we have the curve$\frac x7=\cos^7t$,$\frac y7=\sin^7t$Now I know that$\sin^2x+\cos^2x=1$. So$\cos^2=(\frac x7)^{\text{some exponent}}$. What is that exponent? How do you work it out? 1answer 38 views ### Parametric curve, Write it in cartesian form, giving$y$explicitly in terms of$x$[closed]$x=4\ln(t)y=2t$Write it in cartesian form, giving$y$explicitly in terms of$x$. 1answer 19 views ### Parametric Equation of Cycloidal Sine Curve I am trying to find the parametric equation of a sine curve, which oscillates around a circle as it's$x$-axis. I have done preliminary approximations using Epicycloid parametric equations for the top ... 2answers 32 views ### An equation with a parameter Given the equation$(|x+1|+|x-a|)^2-2(|x+1|+|x-a|)+4a-4a^2=0$find all possible$a$such that this equation has only one solution. I wanted to solve it like this: ... 1answer 27 views ### 2D parametric equation for an arc between two points with a start angle What's a parametric equation (eg.$(x,y)=(\cos(t \cdot 2\pi),\sin(t \cdot 2\pi)$plots a circle where$t$is the 'time' along the circle) that draws an arc between the two points$(x_0,y_0)$and ... 1answer 266 views ### Parametric integration negative area? I know there is a question very similar to mine already here Why does using an integral to calculate an area sometimes return a negative value when using a parametric equation? , but I am still a bit ... 4answers 380 views ### Horizontal tangent line of a parametric curve Suppose$x=t^2,y=t^3$is a parametric curve. Here's a quote from my textbook: The origin, which corresponds to$t=0$, is a singular point of the parametric curve, because$dx/dt=2t,dy/dt=3t^2$are ... 1answer 21 views ### How to find parametric equation between two points in line integral? [In this example how can we find parametric equations of x and y.] [1] [question]: http://i.stack.imgur.com/lTOnW.png [1] [Solution]: http://i.stack.imgur.com/l8ao7.jpg 1answer 18 views ### Convert line parametrization into two equations Consider the following parametrization on$\mathbb{R}^3$$$g(t) = (t^2,t\cos(t),t\sin(t))$$ This is a line, and as such can be characterized by two equations. I already found the first one to be ... 0answers 13 views ### Derive the parametric form of the locus of point where difference between distance to two points is constant Given two points$P_1=(x_1,y_1)$and$P_2 = (x_2,y_2)$, the locus of the point whose (signed) difference between the distance to the two points is a constant$\Delta$is one branch of a hyperbola ... 2answers 34 views ### Parametric version of a simple equation I have a simple relation that I need to plot in a plane. I could do it, but I believe that I don't get the best way. A plane curve is defined implicitely by the following equation : ... 1answer 23 views ### Parametric Equations: Having trouble with finding two tangents (Calculus) [duplicate] curve C defined by these parametric equations$x = t^3 - 3t^2y = t^3 - 3t$I need to find the equations of two tangents at the point$(-4,2)$I have attempted to solve this problem myself but I ... 1answer 19 views ### Deriving parametric equations for a cubic equation I've been looking at elementary cubic equations for curves and seem to understand them well enough. Going the other way and driving parametric equations has been mystifying. For example: given a ... 2answers 714 views ### Reverse direction of parametric equation For the graph$y = \sqrt{x}$the normal parametric equations would$x = t^2$and$y = |t|$. However, the direction for that graph would be going from infinity to zero when$t \leq 0$and zero to ... 0answers 26 views ### Graphing/visualizing a complex parametric plot without using mathematica I am trying to visualize the parametric plot in$\mathbb{C}$of the curve$\gamma$defined for$t\in[-\infty,\infty]$as $$\gamma(t)=\exp\left(-t^{2}+\frac{t}{\sqrt{1+t^2}}i\right).$$ I think I find ... 1answer 37 views ### What's the name of this simple, closed, planar curve? A simple, closed, planar curve can be given by the following parametric function: $$\gamma(t)=\left(\cos t,\sin t+\frac{\sin^2t}{2}\right)$$ This function on$t=0$to$t=2\pi$gives the following ... 0answers 24 views ### How to determine the smallest period of a parametric curve? Consider the polar function$r(\theta) = \sin(3\theta)$, and the parameterization of its graph given by$x = \sin(3\theta)\cos(\theta), \;y=\sin(3\theta)\sin(\theta)$. Upon inspection, one can observe ... 2answers 4k 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$r⃗ (7)=(1,4,7)$, ... 1answer 28 views ### Finding parametric equations of rectangular equation Is there a general process to follow when finding the parametric equations of a normal rectangular equation ? I know that one rectangular equation might have many parametric equations, but are there ... 0answers 71 views ### Polynomial parametrization of a quadric with two given points Let$X^1, X^2 \in \mathbb{R}^3$be two distinct points of the quadric surface defined by the implicit function $$\phi(X)= X^T\cdot A\cdot X + b^T \cdot X+c=0,$$ where and$A$,$b$and$c$are ... 2answers 71 views ### Parametric Surface A surface is given by $$r(u,v) = \langle u, v^2, uv\rangle$$ (a) Evaluate the unit normal vector,$\vec n$, to the surface at the point corresponding to$u=2$and$v=1$. I've done this by ... 0answers 73 views ### Parametric Interpolation in the Plane Given$i+j$points in the plane, when can we find$x(t),y(t)$, polynomials of degree$i$and$j$respectively such that the parametric curve$(x(t),y(t))$goes through each point? We can do this ... 1answer 23 views ### finding cartesian equations of parametric equations find the Cartesian equation for the parametric equation $$x=\frac{1}{\sqrt{1-t}} \text{ and } y=\frac{t}{1-t}$$ I tried cross multiplying but I cant seem to find the equation in terms of$t$to ... 0answers 37 views ### Does anyone known the parametric equations for Cloud Gate? I would like to use Mathematica to plot the famous Chicago "Bean." I couldn't find parametric equations anywhere and was wondering if anyone knew them. Thanks! 1answer 22 views ### Show that the line with parametric equations don't intersect Show that the line with parametric equations$x = 6 + 8t$,$y = −5 + t$,$z = 2 + 3t$does not intersect the plane with equation$2x − y − 5z − 2 = 0$. To answer this do i just plug in the$x$,$y$, ... 1answer 37 views ### Find arc length of$(x-1)^{2/3}+(y-2)^{2/3}=1\$
I'm trying to find the arc length of the curve defined by $$(x-1)^{2/3}+(y-2)^{2/3}=1$$.My first approach was try to set 'y' in terms of 'x' and then apply the formula ...