# Tagged Questions

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

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### How do I detect collisions in a parametric equation$?$ (Lissajous curve)$?$

Let's say you have a simple parametric equation where $x= \sin(3t)$ and $y=\cos(7t).$ This is a pretty simple parametric equation that generates a relatively complicated Lissajous figure. You can ...
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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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Can you help me in finding the analytical expression of a function $f_\alpha(\theta)$, with one parameter $\alpha=(0,1)$ by which one can continously transform a sawtooth curve into a sinus? With $\... 1answer 51 views ### Find the equation of the locus of R if the chord$PQ$passes through$(0,a)$The parabola is$x^2=4ay$Information given: Points of P$(2ap, ap^2)$, Q$(2aq,aq^2)$, and R$(2ar, ar^2)$lie on the parabola$x^2=4ay$. The equation of the tangent at P is$y=px-ap^2$The ... 0answers 41 views ### Finding the locus of a point R The two points$P(2ap,ap^2)$and$Q(2aq,aq^2)$are on the parabola$x^2=4ay$The equation of the tangent to$x^2=4ay$at an arbitrary point$(2at,at^2)$on the parabola is$y=tx-at^2$. The tangents ... 1answer 55 views ### Prove that$p^2+pq+2=0$The information given is that a point$P(2ap,ap^2)$on the parabola$x^2=4ay$. The normal to the parabola at P intersects the parabola again at$Q(2aq,aq^2)$. O is the origin of the graph. The ... 0answers 24 views ### Show that TU is perpendicular to the axis of the parabola. The parabola is$x^2=4ay$Show that TU is perpendicular to the axis of the parabola. Information given: Points of P$(2ap, ap^2)$, Q$(2aq,aq^2)$, and R$(2ar, ar^2)$lie on the parabola$x^2=...
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 ...