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.

learn more… | top users | synonyms (3)

2
votes
2answers
129 views

Trains describing a parabola

From the train station – the point S – originante two tracks, i.e. rays, which do not lie on a common straight line. Along these move two trains, which are line segments. On the first track a train is ...
1
vote
1answer
39 views

Theory of tangents and normals of an ellipse

What are the number of distinct normals that can be drawn to an ellipse from a point inside ,on and outside an ellipse?
0
votes
1answer
35 views

Geometric or analytic proof that in hyperbola, $c^2=a^2+b^2$

How to prove (geometric or analytic) that in hyperbola $c^2=a^2+b^2$? Given that $a$ is the undirected distance of the center to one of the vertices, $b$ is the undirected distance of one of the ...
0
votes
0answers
14 views

What is the best method to find common tangents to two second degree curves?

Often I found myself making my life hard finding common tangent to second degree curves, for example what I would do in case of the following example: Find common tangents to ...
0
votes
0answers
20 views

Find coordinates of vertex and equation of parabola [duplicate]

A parabola has its focus at $(0,4)$. Its directrix is $y = -4$. Q) Find the coordinates of the vertex and write the equation of the parabola. Thank you!
0
votes
0answers
65 views

How to draw an ellipse, given its center, its major radius and two arbitrary points from its perimeter?

I'm trying to write as practice a program where I could visualize a circle being freely moved around in space, and long story short is that I ended up with this problem that I could not solve Besides ...
0
votes
1answer
39 views

Use the pseudoinverse to find the conic section of best fit to the data

I am working on a group project and none of us can figure out how to find the answer. Our professor insists that all of our work be done in maple. The problem is: Use the pseudoinverse to find the ...
1
vote
1answer
51 views

How many non-collinear points determine an $n$-ellipse?

$1$-ellipse is the circle with $1$ focus point, $2$-ellipse is an ellipse with $2$ foci. $n$-ellipse is the locus of all points of the plane whose sum of distances to the $n$ foci is a constant. I ...
0
votes
1answer
36 views

Parabola - How far from the thrower does the ball strike the ground?

The height of a ball thrown in the air is given by $h(x) = \frac {–1}{12} x^2 + 6x+ 3$, where x is the horizontal distance in feet from the point at which the ball is thrown. c. How far from the ...
1
vote
2answers
63 views

Find the locus of points whose distances from the line $y=\sqrt3x$ and x-axis are equal.

Find the locus of points whose distances from the line$\hspace{0.2cm}$ $y=\sqrt3x$$\hspace{0.2cm}$ and x-axis are equal. My solution:I start with the following ...
0
votes
1answer
117 views

Parabola investigation

Edit 4: I added the below picture for clarity I'm trying to figure out how to find the angle between the red line and the blue line, but I have no idea how to start. (I have a feeling that this ...
0
votes
3answers
51 views

Using trig identities to change from parametric to Cartesian equation

$$x=\sin t\\ y= 3\cos (3t)$$ Find $y$ in terms of $x$. I have graphed the function and it appears to follow $y(x)=-4x^2 +2$ from $-1\le x\le 1$ and $-2\le y\le 2$ . Thanks
2
votes
2answers
38 views

What's the parametric equation for the general form of an ellipse rotated by any amount?

What's the parametric equation for the general form of an ellipse rotated by any amount? Preferably, as a computer scientist, how can this equation be derived from the three variables: coordinate of ...
0
votes
0answers
58 views

I need some ideas regarding working model in mathematics. The topics are conics and vectors.

Hi can someone suggest me some working mathematical models under the topics conics and vectors. It should be 12th standard level. (Higher Secondary). I am trying to help my juniors to do this project. ...
0
votes
1answer
17 views

Parabola equation expressed after x

Sorry for the bad title, as English is not my main language. Let me explain better what I mean. I have this equation of parabola: $y = x^2 + 4x $ What I want to do is get the $x$ in one side and ...
1
vote
1answer
29 views

Polar correlation and conics in $\Bbb RP^2$

I'm stuck on a small detail in Proposition 1.2.8 in Geiges' Introduction to Contact Topology. Let $C$ be a conic in $\mathbb{R}P^2$ given by $q^tAq=0$, where $A$ is a nonsingular, symmetric 3x3 ...
0
votes
1answer
31 views

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: $x = t^2, y = 2t$
0
votes
0answers
83 views

Ellipsoidal Decomposition: Finding ellipsoids whose sum contains a given ellipsoid

We have a known ellipsoid $E\left(q,Q\right)$ in a 2D space. $q$ represents the center of the ellipsoid and $Q^{-1}$ is the weight matrix. The general equation of the ellipsoid is given as: ...
1
vote
1answer
26 views

Parabola - equation from three points

Question: Find the equation of the parabola whose axis is parallel to the y-axis and which passes through the points (0,4) (1,9) and (-2,6) Well as the parabola has its axis parallel to the y-axis ...
0
votes
2answers
103 views

Relation of ellipse semi-axes with rotation angle and projection length

In the following setup, assume $w$ (length of the projection of the ellipse) and $\theta$ (the rotation angle) are known. I want to know what equation(s) do I have here that helps me to derive the ...
2
votes
1answer
30 views

finding out wheter point is inside ellipse

I'm working on a way to determine if given point is "inside" given ellipse, the problem is I've already forgotten all the related mathematics and don't have time to relearn it and find a way to do it. ...
1
vote
3answers
53 views

How to find the outermost points in an ellipse?

If an ellipse is given in the form: $$ A(x − h)^2+ B(x − h)(y − k) + C(y − k)^2 = 1 $$ (where A, B, C, h, and k are given) What would be the simplest way of finding the outermost points, by which I ...
5
votes
1answer
79 views

Conic section: What is the coordinate matrix of its bilinear form?

Given is the conic section $x^2 + xy + y^2 + 2x +3y - 3 = 0$. I need to find the coordinate matrix $M_\beta(s)$ of the bilinear form $s: \mathbb{R}^2 \times \mathbb{R}^2 -> \mathbb{R}$. I read ...
0
votes
0answers
34 views

ellipse and segment intersection

I have a rotated ellipse, not centered at the origin, defined by x,y,a,b and angle. Then I have a segment defined by two points x1,y1 and x2,y2 Is there a quick way to find the intersection points?
2
votes
1answer
58 views

what are some applications of modern algebraic geometry to conic sections?

The simplest non-trivial example of an algebraic curve is probably a conic section (ellipse, parabola and hyperbola). At the same time, we also know that development in advanced theory can provide new ...
1
vote
1answer
32 views

Conics Confusion

I'm currently reading through a document about the ellipse. I've attached the provided image and working out. From here, it is easy enough to show that $|OP|\sin\gamma=|FP|\sin\alpha$ using say the ...
0
votes
1answer
32 views

What is the equation of hyperbola

Given that the equation of asymptotes to the hyperbola be: $y=\pm\frac{3x}{2}$ and $b=4$ How to find the equation of hyperbola? I know that asymtotes have the equation $y=\pm\frac{bx}{a}$, ...
1
vote
3answers
47 views

The line is tangent to a parabola

The line $y = 4x-7$ is tangent to a parabola that has a $y$-intercept of $-3$ and the line $x=\frac{1}{2}$ as its axis of symmetry. Find the equation of the parabola. I really need help solving this ...
2
votes
1answer
42 views

Locus on a parabola

How could I find the locus of M as P moves of the parabola. P is.(2at, at^2) . M is the midpoint of the x and y intercepts of the normal through P. So far I was able to find the quation of the normal ...
1
vote
2answers
29 views

Degenerate conics

I was studying about the discriminant of a conic and got to the case where it equals 0. The book I'm referring to says that such a case means that the equation represents a parabola, a pair of ...
0
votes
0answers
20 views

How to draw the reciprocal polar of one ellipse w.r.t. another one

I know that the reciprocal polar of one ellipse w.r.t. another one is a hyperbola obtained as the envelope of all polars from points lying in one of the ellipses w.r.t. the other. My question is: how ...
1
vote
0answers
23 views

Catenary and parabola minimum comparison

Do the catenary and a parabola that approximates the catenary, have the same minimum (maximum sag)? IF plotted, it looks to me they do, and that they only difer somewhere on the "slope". (sorry for ...
0
votes
2answers
40 views

Ellipse as projection of a disk - function describing ellipse diameter with disk rotation?

Say I have got a disk of radius $r$ and a plane $p$ in $3D$ space. The disk is "aligned" to $p$ and lies at an arbitrary distance, so that its orthogonal projection on $p$ is an identical disk of ...
2
votes
3answers
68 views

Solving $\frac{\mathrm d^2\mathbf{q}}{\mathrm dt^2} = -\frac{\mathbf{q}}{|\mathbf{q}|^3}$

I am reading a set of course notes and it has this example of a system of differential equations given by $$\frac{\mathrm d^2\bf{q}}{\mathrm dt^2} = -\frac{\bf{q}}{|\bf{q}|^3}$$ All it says is that ...
0
votes
0answers
15 views

How to draw a border at a specific distance from a cylinder outline

I have a small cylinder (Cylinder A) with its minor radius of A. Minor radius measures the minor radius of the cylinder ellipse. I need to draw a border at a distance of X from the border of ...
1
vote
1answer
24 views

Determining if two general conic sections are tangent to each other

Given two conics in general form $A_ix^2 + B_ixy + C_iy^2 + D_ix + E_iy + F_i = 0$ for $i = 1, 2$, I want to determine if they are tangent to one another, and I'm looking for a method that wouldn't be ...
0
votes
1answer
19 views

$P$ is a point on a hyperbola whose focal points are $F_1$ and $F_2$. $Q$ on the line that bisects $\angle F_1PF_2$. Prove $|PF_1-PF_2|>|QF_1-QF_2|$.

$\require{cancel}$ Sorry for the grammatical mistake in the title; it was needed to keep the title under 150 characters. $P$ is a point on a hyperbola whose focal points are $F_1$ and $F_2$. $Q$ is ...
1
vote
1answer
53 views

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 ...
0
votes
1answer
45 views

finding $\lambda$ when equation of parabola is given

If the equation $\lambda x^2 + 4xy + y^2 + \lambda x + 3y + 2 = 0$ represents a parabola. Then find $\lambda$. I got stuck in this question while solving parabola. Is here anybody who can help me ...
0
votes
1answer
64 views

Prove that the locus is a parabola

The point P(x,y) moves in XY plane such as that its distance from a fixed point (0,-1) is equal to its distance from the line Y=1. Prove that the locus is a parabola. Find it's focus, directrix, ...
0
votes
0answers
23 views

Curvature of track of focal point

Prove: A ellipse pure roll on a line l,show that the centripetal acceleration of F1 is 0 if F1F2∥l.
2
votes
1answer
98 views

Finding the asymptotes of a general hyperbola

I'm looking to find the asymptotes of a general hyperbola in $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ form, assuming I know the center of the hyperbola $(h, k)$. I came up with a solution, but it's too ...
0
votes
0answers
66 views

Predicting Bending of Plywood (Conical Shapes)

I'm building a NASCAR-style banked track for 1/27 scale RC cars, and I'm trying to predict the bends I need to cut to produce the banked track I want. I've already built some simple banked pieces, ...
1
vote
1answer
24 views

General “Conics” of higher degrees?

A general conic has the form $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$. I understand that there are certain properties of this equation that make it special and allow us to classify the different types of ...
1
vote
0answers
45 views

Non linear least square ellipse fitting

I am trying to find a Non linear leasts squares ellipse fit for a set of 100 data points data points $(x,y)$. Now i have found the values of $A,B,C,D,E,F$ according to the conical equation of the ...
0
votes
1answer
29 views

Movable “light” in 3d enviroment

A light-emitting object is suspended in a 3 dimensional environment at a known position (eg: X=0, Y=0, Z=10). The object emits light with a certain beam pattern; it is not omnidirectional. The ...
2
votes
2answers
75 views

“Conic sections” that are really just two straight lines

My teacher was teaching co-ordinate geometry and today he said that the following equation will always represent a conic section:$$ax^2+by^2+2hxy+2gx+2fy+c=0$$ Then he said that if the determinant of ...
0
votes
0answers
34 views

How to find the tangent vector for intersection of two cones?

Let two points $A=(x_{0},y_{0},z_{0})$ and $B=(x_{1},y_{1},z_{1})$ are given vertex of two cones and the generating angle of two cones are $m$. Intersection of two cones could be either an ellipse or ...
2
votes
1answer
73 views

Projective and affine conic classification

I have a doubt on the classification of non-degenerate conics (parabola, ellipse, hyperbola) in projective geometry (my textbook is "Multiple View Geometry in Computer Vision", which, as the title ...
2
votes
1answer
51 views

Conic Sections Parameter set constraints

Given the general equation $Ax^2 + Cy^2 + Dx + Ey + F = 0$, what constraints on the set $\{A,C,D,E,F\}$ will apply if the equation represents a (a) parabola? (b) ellipse? (c) hyperbola? Firstly, I ...