# Tagged Questions

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### Find the parametric equation of the following parabola?

It doesn't give me $2$ equations this time just $1$ and I have no clue what to do; $y^2 = 4x$ ANSWER IN BOOK: $x = t^2, y = 2t$
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### Finding equation of directrix when the parametric equation of parabola is given.

If the parametric equation of the parabola is $( x = t^2 + 1 , y = 2t + 1 )$, then find the equation of the directrix. This was the question in my last test in which I got stuck and wasted much of my ...
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### Intersection between sphere and ellipsoid

I am failing since two days to compute and to plot the intersection of an ellipsoid in parametric notation ...
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### Rotation of conics sections using linear algebra

When given an equation of the form $$Ax^2+Bxy+Cy^2 + Dx + Ey + F$$ where $B \not= 0$ and it is not a degenerate conic, then you can use $\Delta = B^2 -4AC$ to see what type of conic it is, and then ...
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### ratio of tangent to the ellipse

The tangent at point $P = ( a \cos \phi, b \sin \phi)$ on the ellipse $\frac{x^2} {a^2} + \frac{y^2}{b^2}=1$ meets the $x$ and $y$ axes at the points $X$ and $Y$, respectively. Find in terms of ...
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### Relation between ellipse general and parametric equation

I am familiar with the fact that one can relate the eigenvectors and corresponding eigenvalues of an ellipse's quadratic equation matrix, to the pose of a circle in 3-space. When say quadratic ...
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### Parabola in parametric form

Show that the following system of parametric equations describes a line or a parabola: $$\begin{cases} x=a_1t^2+b_1t+c_1 \\ y=a_2t^2+b_2t+c_2 \end{cases}, t\in\mathbb{R}.$$
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### Parallel Curves to a Parabola

I have been modelling parallel curves to a parabola and realise if the parallel curve to a parabola is offset enough then the curve will overlap. I came across this research paper to explain why a ...
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### Find parametrizations for Circles and Ellipses

a) The portion of the circle $x^2 + y^2 = 4$ traversed clockwise from $(-2,0)$ to $(0,2)$ b) The part of the ellipse $(x^2)/(4) + (y^2)/(9) = 1$ that lies above the line $y = 0$, traversed clockwise. ...
What is the method of find the parametric equations for all types of parabolas? And in both directions? So if I had 2 points: Parametrise from A to B Point $A = ( \frac{3}{\sqrt2} , 9 )$ and Point ...