# Tagged Questions

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

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### Parametrization of a hypocycloid

How do I prove that a hypocycloid, which has equation $$x^{2/3} + y^{2/3} = a^{2/3}$$ can be parameterized by $$x = a\cos^3(\theta),\qquad y = a\sin^3(\theta)$$? The problem assumes that it is true, ...
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### Length and revolved surface area of parametric curve

Can someone verify this for me?
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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 ...
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### Convergence of a sequence depending on parameter

My math teacher gave us this exercise for homework: Given $a \in [-3, \infty),$ a given sequence $(x_n),$ with $x_n = \left(\frac{a^n+2}{3^n+4}\right)$ Determine $a$ so that the sequence $(x_n)$...
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### How to set control points for spline curves

I've written a program that calculates points on spline curves (including Hermite, Bezier, and B-splines) and plot the curve on the screen (the curve is plotted on an html canvas using javascript). ...
Let $P(ap^2,2ap)$ and $Q(aq^2,2aq)$ be two points on the parabola $y^2=4ax$ such that PQ is the focal chord. Let $A(at^2,2at)$ and $B(as^2,2as)$ be two other variable points on $y^2=4ax$. a) Show ...
### Equations of an Oblique Circular Cone ($2$ circles are known)
I am trying to determine the parametric equations for an oblique circular cone with no success, as is shown in the figure above. Top circle is at point $(31,30,125)$ with a radius of $20$, and bottom ...