Questions on conic sections and their properties; the curves formed by the intersection of a plane and a cone. Circles, ellipses, hyperbolas, and parabolas are examples of conic sections.
1
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1answer
15 views
Maximum Y in a rotate ellipse with a, b and phi
We have major axis, minor axis and the phi between major axis and y axis in a rotated ellipse.
How can we find the maximum y?
3
votes
1answer
204 views
How do I get a tangent to a rotated ellipse in a given point?
I have just graduated from a school you would call High School and even though we talked about tangents to ellipses, we never covered rotated ellipses. So, what I am looking for, is a formula for a ...
2
votes
1answer
35 views
Finding eccentricity of an ellipse from latus rectum
The latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is the same as latus rectum of a parabola $y^2=4cx$ . Find eccentricity of the ellipse .
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vote
2answers
123 views
major and minor axis of ellipse, $\phi$ (degree from x axis)
The ellipse is:
$$
x(t)=a \cos(wt-c)\\
y(t)=b \cos(wt-d)
$$
What are:
major axis length
minor axis length
angle of major axis with $x$ axis?
the parametric form ? $(ax^2+by^2+cxy+dx+fy+...=g)$
1
vote
3answers
48 views
Would a circle overlap a parabola's bottom by more than just its vertex?
I mean, out of the condition that a circle actually crosses the parabola.
My question is when a circle is "inside" a parabola, would it touch part of the parabola other than just the parabola's vertex ...
0
votes
1answer
21 views
Parabolic projectile equation demonstration question
I was looking at a book of physics and, it will sound dumb, but while I know that the maximum height equation of a projectile is max=(v·senα)/2g, I can't understand how do you get there from ...
4
votes
3answers
2k views
Calculating a Point that lies on an Ellipse given an Angle
I need to find a point (A on this diagram) given the center point of the ellipse as well as an angle. I've been melting my brain all day (as well as searching through questions here) testing out ...
2
votes
0answers
30 views
How to find a point in an ellipse given the angle
I found a couple of formulas but I can't transform them in code.
From the answer in Calculating a Point that lies on an Ellipse given an Angle , for instance, I get to:
...
1
vote
1answer
41 views
Find next point in ellipse given the chord length
I would like to draw a cloud programmatically. For this reason I need to know where to draw the next circle around the ellipse.
Given the chord (circle radius), how can I calculate the next point in ...
1
vote
1answer
54 views
Solve for an Ellipse Tangent to 2 Lines [duplicate]
I'm trying to automate creation of a curve in PowerPoint.
Here's an image of what I'm working towards:
I'm trying to show a diagram of a rocket trajectory from a launch site on Earth to a circular ...
1
vote
1answer
29 views
Find equations of the ellipses given conditions on the directrices, foci, and vertices
The ellipses have their centers at the origin and their major axes on the $x$-axis. Find the equation:
with distance between directrices $27$, and between foci $3$;
with a focus at $(-\sqrt{13},0)$ ...
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vote
1answer
16 views
Find the equation of the hyperbola given foci and the minor axis
first time posting and using the site. I have a quick problem that I need some help with. I need to find the equation of a hyperbola given the foci and the length of the minor axis.
The foci ...
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vote
2answers
48 views
Angles and ellipse (proof)
First of all, sorry for my poor English! Can you please help me? I'm trying to prove that, given a point P at an ellipse.
Please help me prove that the angles are equal.
Thanks!
0
votes
1answer
67 views
hyperbola: equation for tangent lines and normal lines
Find the equations for
(a) the tangent lines, and
(b) the normal lines,
to the hyperbola
$y^2/4 - x^2/2 = 1$ when $x = 4$.
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vote
2answers
40 views
conic sections, ellipse
A particle is travelling clockwise on the elliptical orbit given by
$$\displaystyle \frac{x^2}{100} + \frac{y^2}{25} = 1$$
The particle
leaves the orbit at the point $(-8, 3)$ and travels in a ...
1
vote
2answers
47 views
How do you find the distance between two points on a parabola
So I've been wanting to figure out a formula for an odd pattern I found... but to write a proof, I need to know one thing...
How do I find the distance between two points on a parabola?
Like, if I ...
0
votes
2answers
313 views
Convert ellipse parameter from General parametric form to General polar form
I am facing problem to convert ellipse standard parameters. Everything I say here is refer to http://en.wikipedia.org/wiki/Ellipse
I know what are the General parametric form parameter . Lets call ...
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votes
2answers
34 views
Finding the tangents common to two rotated ellipses?
Is there a way to find the four tangents that two rotated ellipses share?
I believe that if two ellipses do not intersect and do not contain one another, they will have four tangents in common and I ...
3
votes
2answers
175 views
A construction using straightedge and compass
Given a circle, it's easy to contruct its center.
The question is: given an ellipse, draw the foci.
I don't know whether it's possible to do this using only straightedge and compass.
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vote
2answers
54 views
How to calculate ellipse sector area *from a focus*
How do you calculate the area of a sector of an ellipse when the angle of the sector is drawn from one of the focii? In other words, how to find the area swept out by the true anomaly?
There are ...
5
votes
1answer
45 views
Determine if a conic is degenerate with the determinant.
There is a natural bijection between conics (written as homogeneous quadratic) and 3x3 matrices:
$$C=aX^2+2bXY+cY^2+2dXZ+2eYZ+fZ^2\Leftrightarrow \left(\begin{array}{ccc}
a&b&d\\
...
3
votes
2answers
37 views
How do different definitions of ellipse translate to the same thing?
There are 2 definitions of an ellipse that I know.
One definition goes:
The locus of a point moving in a plane such that the ratio of its
distances from a fixed line (directrix) and a fixed ...
1
vote
1answer
35 views
Car parking problem
I want to park my car doing similar to the one in the image. But I want to define a curve such that I park the car at once (without going forward, always backward). Suppose that the place that I want ...
1
vote
1answer
24 views
Application of derivative - tangents to latus rectum
Drawn thru the focus of parabola is a chord perpendicular to the axis of the parabola. Two tangent lines are drawn through the points of intersection of the chord and the parabola. Prove that the ...
0
votes
3answers
58 views
How to write this conic equation in standard form?
$$x^2+y^2-16x-20y+100=0$$
Standard form? Circle or ellipse?
2
votes
1answer
20 views
How to prove and derive coefficients that an exponential whose base decreases exponentially is a parabola
Suppose I have a function defined by this recurrence-relation:
$$R(0) = r$$
$$R(n) = R(n-1) * (1+G)d^{n-1}$$
Here r is a base value, G is a base growth rate (G>0) and d is a decay in the growth rate ...
0
votes
0answers
92 views
Conversion from Standard Ellipse Function to General Ellipse Function
I wonder if anyone can assist/show me how to complete this task...
I have the following equation which models a dual axis magnetic field:
$$\begin{equation} B_{H}^2 = B_x^2 + B_y^2 ...
2
votes
1answer
70 views
proof that intersection of two conic sections will intersect at at least two points.
In the following equation ρ(x,y) returns a constant value for a given coordinate.
n is the normal vector to the surface of the form [P,Q,-1] and s is a direction vector.
Using s = [Sx,Sy,Sz], the ...
1
vote
1answer
163 views
Formula and foci of ellipse formed by intersection of ellipsoid and plane
I have the ellipsoid $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ and the plane $n_xx+n_yy+n_zz=0$. They intersect along an ellipse.
1) What is the formula of the ellipse, and
2) What is the ...
3
votes
1answer
402 views
Relationship between ellipsoid radii and eigenvalues
I should start by saying that I haven't done algebra for very long time. I recently have some work related to algebra, so I need some help to speedup.
I went through a theorem in the book stating the ...
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0answers
30 views
Representing conic sections as straight lines
Is there a projection that projects any conic section in a two dimensional orthogonal coordinate system with a focus at the origin into a potentially infinite set of parallel straight lines in a two ...
6
votes
11answers
5k views
Derivation of the formula for the vertex of a Parabola
I'm taking a course on Basic Conic Sections, and one of the ones we are discussing is of a parabola of the form
$y = a x^2 + b x + c$
My teacher gave me the formula:
$x = -\frac{b}{2a}$
as the $x$ ...
1
vote
2answers
129 views
Area of ellipse given foci?
Is it possible to get the area of an ellipse from the foci alone? Or do I need at least one point on the ellipse too?
3
votes
2answers
37 views
What is the rationale for the factor of $4$ in the Conics parabola equation?
The Conics form of a parabola equation is $4p(y-k)=(x-h)^2$ where $(h,k)$ is the vertex of the parabola and $p$ is the distance from the vertex to the focus. (Which is also the same distance from the ...
2
votes
2answers
303 views
A hyperbola as a constant difference of distances
I understand that a hyperbola can be defined as the locus of all points on a plane such that the absolute value of the difference between the distance to the foci is $2a$, the distance between the two ...
0
votes
1answer
31 views
Determine the Angle of an point in an Ellipse
I would like to know how to determine at which angle a point lies in an ellipse. Suppose I have an ellipse with semimajor and semiminor of 10 and 5 (see ...
1
vote
1answer
51 views
Different curves
I stuck on a following question.
The curve is given by:
$(3-k)x^{2}+(7-k)y^{2}+9x+9y+7=0$ For which parameter $k$ k the curve will present
1)ellipse or circle
2)parabola
3)hyperbola
Thanks a lot!
1
vote
2answers
41 views
Computing the Semimajor and Semiminor axis of an Ellipse
I have the equation of the ellipse which is $\frac {x^2}{4r^2}+\frac{y^2}{r^2}=1$ Putting the (4,2) point on the ellipse we get $r^2=8$ so we get the equation $\frac {x^2}{32}+\frac {y^2}8=1$ and the ...
0
votes
2answers
79 views
Finding the Width and Height of Ellipse given an a point and angle
I have ellipse, lets say that the height is half of its width and the ellipse is parallel to x axis. then the lets say the center point is situated in the origin ...
0
votes
1answer
51 views
Finding a,b of elipse
Given $x^{2}+y^{2}=R^{2}$, so that we multiply every $x$ by $a$ and every $y$ by $b$, $(a>b)$
And the distance between the focuses of this locus is $48R$, and the area of the rhombus which ...
2
votes
1answer
43 views
Minimum distance between $x = -y^2$ and $(0,-3)$
Find the minimum distance from the parabola $x + y^2 = 0$ (i.e. $x = -y^2$) to the point $(0,-3)$.
This is a homework question. When I try to use the derivative and substitute $-y^2$ for $x$, I ...
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vote
1answer
87 views
Incomplete elliptic integral of the second kind and the arc length of an ellipse - does a `simple` relation exist?
Short introduction
For a calculation I am working on I need to determine the arc length $l$ of a part of an ellipse in terms of the major axis $2a$, the minor axis $2b$ and the angle $\phi$.
I ...
3
votes
1answer
327 views
Intersection of conics using matrix representation
I came across a very interesting section of a wikipedia article on conics: http://en.wikipedia.org/wiki/Conic_section#Intersecting_two_conics
I am trying to work out a couple of examples to add to ...
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vote
0answers
29 views
How can I find $\int{\sqrt{\left(b^2-1\right)x^2+1\over-x^2+1}}dx$?
I got this from the perimeter of an ellipse. I came up with the formula: arclength of f(x) for x from a to b=$\int_a^b\sqrt{f'(x)^2+1}dx$. Since an ellipse has the equation: $$\left({x-h\over ...
2
votes
1answer
107 views
How do we know $\pi$ is a constant? [duplicate]
How did the ancient Greeks discover that the ratio of a circle's circumference to its diameter is constant? It does not seem so intuitive. Thanks!
1
vote
1answer
44 views
Turning an ellipse into a parabola
Today I was discussing circles, ellipses, hyperbolas, and parabolas in my precalculus class. We did the usual: completing the square, finding the center and radius (radii), etc. etc. But I like to ...
13
votes
8answers
3k views
What is the real life use of hyperbola? [closed]
I was doing hyperbola ,I was thinking does it have any real life uses or it just a mathematics theory?
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2answers
63 views
Good books on conic section.
Can anybody suggest me good books for conics section.I want it for IIT-JEE mains and advanced and also for ISC. It should be available in India .
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1answer
118 views
How to find equation of parabola when we only know the equation of latus rectum and coordinates of vertex?
Suppose the equation of latus rectum is x=4 and the vertex is (2,3). I am confused wouldn't there be many parabola with this same vertex and latus rectum.If not how to find the equation?
The answer ...
8
votes
3answers
531 views
an important property of an ellipse
Good morning everybody.
I would like to know the proof of the following observation on the ellipse.
A circle is drawn with the right latus rectum as diameter. Another circle is drawn with its ...
