# Questions tagged [parametric]

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

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### Find the parameterization of shadow cast on plane

Suppose there is a light source at $(0, 0, 8)$. Consider the line segment $r(t) = \langle 3-3t, 1+t, 2+2t\rangle, 0\le t\le1$. Find the shadow cast by the line segment on the plane $x+y-2z=8$ I have ...
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### Is the Stokes-Carten theorem suitable for knotted manifolds

I am currently trying to discretise a torus knot onto a square lattice grid. My method of achieving this has been to first use the Torus knot parametric equation, then define a circle that follows the ...
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### Intersections of the involute of a circle with the $x$-axis

I am looking for a parametrization of the involute of a circle in order to perform a least-squares fitting to some spiral data points. I started with the usual parametric form of the involute, in ...
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### When do two quadratic equations have exactly one common solution?

I have stumbled upon the following two exercises: For $a,b \in \mathbb{Z}$, consider $A=\{x\in\mathbb{R} | x^2+2ax+b=0\}$ and $B=\{x\in\mathbb{R} | x^2+2bx+a = 0\}$. Let $k$ be the number of elements ...
• 561
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### Is there a parametric equation that describes the D-shaped? [closed]

How can a curve that looks like a D be described by a parametric equation?.It can be defined as in the figure below and also a parametric equation. I don't know if Fourier series can be used to ...
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### Where to find velocity and radius of vectors for animation of Fourier parametric shape

I have a parametric equation where the parameters are sums of sines and cosines such as $\left(3+4\cos2t+2\sin2t,7+0.8\cos2t-0.5\sin2t\right)$. I want to animate this with some vectors, rotating at a ...
1 vote
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### Parametric Bootstrap confidence interval does not contain estimated parameter - Python code [closed]

I have some artificial data with only one feature in the covariates and an integer response on which I perform Poisson regression (see below for a plot). I would like to obtain 95% confidence ...
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### Parametric families of area-preserving curves?

I have an interesting PDE problem that I would like to solve. Consider the diagram below. I would be very interested to hear about whether there are any "nice" families of parametric curves ...
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1 vote
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### Is there an easy way to combine a piecewise curve into one curve?

The problem related to shape below. I need to find a parametric equation curve that is split into four different equations depending on the range. How can piecewise equations be combined into a single ...
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### Nonlinear cartesian equation to parametric equation

how can I parametrize the following equation? Not sure what techniques I should use here since it's my first time. $\begin{cases} M_1 : z=16-3x^2-y^2 \\ M_2 : z=(x-4)^2+3y^2 \end{cases}$
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### vector questions finding another line with the two given lines.

I have questions about this problem. The vector equation of the lines L1 and L2 are r=(15,11,6)+t(6,3,2) and r=(0,7,-4)+s(-3,2,-6) respectively. Let A and B be the points on L1 and L2 with parameters ...
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### How to find the radius of the circle such that it intersects one ellipse at only one point? [duplicate]

I have a circle centered at (0, 0) with an unknown radius r. I also have a shifted and scaled ellipse (s.t. $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$). I want to find the radius that intersects ...
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### Distance and Arc Length (Math GRE)

A circular helix in $xyz$-space has the following parametric equations, where $\theta \in \mathbb{R}$. $x(\theta)= 5\cos(\theta)$ $y(\theta)=5\sin(\theta)$ $z(\theta)=\theta$ Let $L(\theta)$ be the ...
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### Is there a way to modify the solid of revolution integral to allow for solids of increasing and decreasing radius?

I am doing a project on tori as they relate to pool floaties and the volume of a normal torus can be calculated by the solids of revolution integral on a circle, Is there a way to modify the integral ...