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Questions tagged [parametric]

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

In mathematics, a parametric equation of a curve is a representation of this curve through equations expressing the coordinates of the points of the curve as functions of a variable called a parameter. This contrasts with implicit equations that define a curve as the zero set of some equation in the coordinates.

The parametric forms of curves are well-suited for drawing on a computer, while their corresponding implicit forms are useful for analytic manipulations (intersections, etc.)

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Parametric equations - plotting graph

I was wondering how can one draw a graph (at least schematic) from given parametric equation, For example I took $$x=a\cos^3(t)\qquad \text{and}\qquad y=a\sin^3(t).$$ Initially I tried to find solution of $x=y$. And then where it get zero, but I…
pde
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Line intersecting spheroid

I have two planes $(A): u_{1}x + v_{1}y + w_{1}z = d_{1}$ and $(B): u_{2}x + v_{2}y + w_{2}z = d_{2}$. They intersect together, then they yield a line $(L)$ that has a direction vector $M (x_{M},y_{M},z_{M})$ $M$ is the cross product of the normal…
Khaled
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Show that C is not simple by finding the point where the curve intersects itself

This is the problem that was given to me. After going through google and looking in my book (Stewart Calculus) I am still stumped on this because it is not linear. My next instinct would be to check the derivatives instead of the actual…
MaxAttax
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Derivatives of a parametric equation

Suppose a curve $S$ in 2-D is parameterized by $$S=\{(u(s),v(s)): s\in\mathbb{R}\},$$ where $u$ and $v$ are $C^{1,\alpha}$ for $\alpha \in (0,1)$ with $$u(s+2\pi)=u(s)+2\pi \qquad \text{and} \qquad v(s+2\pi)=v(s) \qquad \text{for all } s \in…
dh16
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Mistake in determining period of a parametric motion

The position of an object in circular motion is modelled by the given parametric equations. Describe the path of the object by stating the radius of the circle, the position at time $t = 0$, the orientation of the motion (clockwise or…
Amy Jones
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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 that for any three numbers $a,b,c$ the…
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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 $P_0(1,\sqrt{3}, 0)$?
Yigit
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Why are the parameterizations of the circle in cartesian coordinates defined in open intervals?

The parameterization of the circle in rectangular coordinates is given by the the following functions $$ y = g_1(x) = \sqrt{(1-x^2)} \\ y = g_2(x) = -\sqrt{(1-x^2)} \\ x = g_3(y) = \sqrt{(1-y^2)} \\ x = g_4(y) = -\sqrt{(1-y^2)} $$ for $-1
user1790813
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Creating a Parametric Equation

The problem is as follows: "In each of the following cases, you will be asked to write down a family of parametric curves that have the property that at $$t = 1$$ we have $$x'(t) = y'(t) = 0$$ but the slope of the curve has the property listed…
asuperbaname
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Finding c in parametric quadratic equation

I tried searching before posting this, but couldn't find anything. I have this parametric* equation : $ x^2 + 54x + 5a^2 = 0 $ They are asking me to find the values of a for which the roots of the equation will be $x_{1} = (1/5)x_{2}$ The things…
Martin Spasov
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How can i translate a parametric equation to cartesian

The parametric equations are : $$ x=16\sin^3(t)$$ and $$y=13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t) $$ with $t$ from $-\pi$ to $+\pi$ so I'm new to this kind of equations and i really don't know how to start the conversion... Can someone help me?
Cristian
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Parametric question of the curve $x^2 + y^2 + 2x - 4y = 0$?

What is the parametric form of the curve above? If I had to solve it, what I would say is that the first step is to complete the square. However, where would I go from there?
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Parameterization of an ellipse

If an object (like a planet) orbits around a more massive object (like the sun) the orbit will be an ellipse with the massive object at one of the two foci of the ellipse. The parameterization $$x(t) = 2 \cos(t), \text{ and } \ y(t) = \sin(t)$$ is a…
user280495
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Finding an equation relating $x$ and $y$ with their respective parametric equations and using its differential?

How can I find the equation relating $x$ and $y$ directly without an additional parameter $t$, which both are related to initially. For example, $\frac{\mathrm{d}y}{\mathrm{d}t} = 2t+1$, $\frac{\mathrm{d}x}{\mathrm{d}t} = 2t-1$, and $y = t^2+t$ , $x…
mathworker123
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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 $x = \sin(4t^{\frac{2}{3}})$ and $y = \cos(0.5\pi t^2)$ over…
louie mcconnell
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