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.

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1answer
48 views

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 ...
2
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1answer
25 views

Finding perimeter of an ellipse accurately

How could you accurately find the perimeter of an ellipse accurately? This formula: $$p\approx 2\pi\sqrt{\dfrac{a^2+b^2}{2}}$$ (Where 'a' is the distance from the center of the ellipse to the ...
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6answers
53 views

To find the distance of a point from ellipse [on hold]

find the maximum and minimum distance of point P(3,-1) from ellipse having equation $x^2 + 4y^2 - 4x + 8y - 8 = 0$
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4answers
38 views

Interesting association between tangent lines of slope one and ellipses

Why is it that a tangent line with slope $1$ to an ellipse centered at the origin will have a transformation of $\pm \sqrt{a^2 +b^2}$ where $a$ and $b$ are the major and minor axis of the ellipse? ...
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0answers
18 views

Finding the distance from a parabola (ballistic trajectory) to a point (for use in collision detection)

I need to have some form of collision detection / prevention for an object moving along a ballistic trajectory and a second stationary object on the same plane plane. The ballistic trajectory is ...
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1answer
16 views

How to identify any point inside or outside the given cone?

The equation of a double circular cone with a vertex $p=(a,b,c)$ with the generating angle $t$ is given by $(x-a)^2+(y-b)^2= \frac{(z-c)^2}{t^2}$ How do I identify the point ...
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0answers
14 views

How to find centre,vertics,foci,focal radii,letus rectum… when exists of a general quadratic equation in x and y

Is there a generalized way( a particular conic section of any shape,for instance an ellipse without determining its major/minor axis) to find the centre,vertics,focus,focal radii,letus ...
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1answer
27 views

How do you sketch a parabola given the equation? [closed]

The equation is $y^2=16x$, and it wants you to sketch the vertex, focus, directrix.
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1answer
24 views

need explanation of what exactly is a directrix & focus?

((I'm not asking why do we need to know conic sections etc.) Like other similar questions.) I actually love math & currently learning conic sections in class, neither my textbook or teacher ...
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2answers
33 views

Area of triangle inscribed in a parabola

How can u prove that the area of the triangle inscribed in a parabola is twice the area of the triangle formed by the tangents at the vertices?
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1answer
22 views

Centroid of triangle formed by co-normal points

How can you prove that he centroid of a triangle formed by 3 co-normal points lies on the axis of the parabola?
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2answers
42 views

Orthogonal tangents to an ellipse [duplicate]

This is the problem I found back in the first year in the university. Suppose we have a non-degenerate (i.e. not a point and not an empty set) ellipse $E\subset \Bbb R^2$. Now define a set $D$ by a ...
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1answer
31 views

The minimum distance from the circle $x^2+(y+6)^2=1$ to parabola $y^2=8x$?

What are the coordinates of the points on the parabola $y^2=8x$ which are at the minimum distance from the circle $x^2 + (y+6)^2=1$?
2
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1answer
26 views

Counting the dimension of a component of $\mathsf{hilb}^{2t+1}_{3}$

Consider the Hilbert scheme $\mathsf{hilb}^{2t+1}_{3}$, parametrizing varieties of degree $2$ and genus $0$ in $\mathbb{P}^{3}_{k}$, with $k$ an algebraically closed field. Consider the component $ ...
3
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1answer
38 views

Locate a point a given distance from another point on an ellipse

Similar to Point on circumference a given distance from another point, but for an ellipse. Unfortunately, the difference is non-trivial. I have an ellipse and a point (C) that is somewhere on the ...
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2answers
36 views

how do i write an equation in standard form by completing the square for $x^2 -9y^2-4x-18y=14$

I'm really having trouble with completeing squares i can solve for circles and ellipses but i can't seem to understand hyperbolas or parabolas, help would be deeply appreciated.
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1answer
14 views

Calculating an Ellipse given the Orbital Eccentricity and a Vertex?

I know that the formula for Eccentricity is e = c/a where c is the distance from the center to a focus and a is the distance from that focus to a vertex. I know the distance from the center of the ...
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1answer
28 views

Finding locus of centroid

Let AB be a chord of circle x^2 + y^2 = 3 which subtends 45 angle at P where P is any moving point on the circle. Then find the locus of centroid of triangle PAB Any help would be appreciated
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1answer
12 views

Finding Radical centre problem

Suppose 3 circles are drawn taking the 3 sides of a triangle as their diameters, what would be the radical centre of these circles? The options are circumcenter, orthocenter and incenter Any help ...
2
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1answer
17 views

Locus of centre of variable circle

I am not able to figure out this question What is the locus of the centre of a circle which touches a given line and passes through a given point, not lying on the given line? I think it's a ...
0
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1answer
35 views

Intersection of a 45 degree angle and an ellipse

If you are looking at the upper right quadrant of an ellipse centered at $(0,0)$, with $a=1$ and $b = 0.6$, and there is a $45$ degree line drawn from $(1, 0.6)$, how would I find the $(x,y)$ ...
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1answer
44 views

Identify the locus.

Let $A,B,C$ lie on a straight line. $B$ is lying between $A$ and $C$. Consider all circles passing through $B$ and $C$. The point of contact of the tangents from $A$ to these circles lies on ..... We ...
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1answer
33 views

If an ellipse has two radiuses, is there something like it, but with three or more radiuses?

If we say that a circle has one radius, and an ellipse has two, can I define figures that have three, four, or more radiuses? Also, how can I get that "radius"? In an ellipse that is 10 at its ...
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1answer
30 views

How to find the equation of a parabola with vertex on the line y = -3x?

Its axis are parallel to the y-axis and passing through (-7,13) and (5,1).
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2answers
51 views

Find the tangents to the following curve from the given point.

2x^2 + y^2 = 54 from (10,1) P.S. I still don't study calculus. This lesson is from analytic geometry and I have no idea how to solve it because my professor didn't teach it. So if someone could tell ...
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0answers
42 views

Equation of intersection of two cones

The equations of two cones are given; $(x-x_{0})^2+(y-y_{0})^2=\frac {(z-z_{0})^2}{m^2}$ and $(x-x_{1})^2+(y-y_{1})^2=\frac {(z-z_{1})^2}{m^2}$ How to find the equations of intersections 1) ...
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1answer
57 views

Find the equation of an ellipse

I have to find the equation of an ellipse which passes through the point $(3, 2)$, has center at the origin and major axis along the y-axis, i.e., is a vertical ellipse. No other info is given. I've ...
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3answers
30 views

Solve a system of equations involving two ellipses

Problem #38 asks us to solve the system using either graphing, substitution, or elimination. The only way that I can think of doing this is by graphing. However, is there any easy way to solve this ...
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1answer
34 views

Area of circle formed when sphere is sliced by a plane

First off, when a sphere is cut by a plane, is a circle always formed or does a ellipse get formed in some cases? If a circle is always formed, how do you prove it? Next, how would you find the area ...
2
votes
2answers
63 views

Why does the “T=0” method to calculate tangent work?

Given a random equation of a curve: $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$. Suppose we need to find the tangent to this curve at any point $A(x_1, y_1)$. A method given to me by my professor was the ...
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2answers
110 views

Show that the intersection of a plane…

Show that the intersection of the plane $z = 2y$ with the elliptic cylinder $\frac{x^2}{5} + y^2 = 1$ is a circle. Find the radius and center of this circle. Hint: How can one describe a circle in ...
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0answers
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Number of ellipses to uniquely define a co-centered circumscribing ellipse

I have a bit of a tricky problem that has come up in my engineering research, but I haven't quite got the brains to figure it out, though I've gotten pretty far. Suppose that there is an unknown ...
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3answers
217 views

What is wrong with this method for a rotated and shifted parabola?

$(x+2y)^2=4(x-y)$ Disecting the above parabola is the question. (vertex, axis,tangent at vertex,etc). So at first what I thought of was making its equations at LHS and RHS perpendicular. I thought ...
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0answers
20 views

finding the center of an ellipse given 3 points and 2 tangent lines

I'm given a vertex on the minor axis- point (0,7), two points on the ellipse, (-15,0) and (15,0) and the tangent line in point (-15,0) has an angle of 65° to the x axis (so actually two tangent ...
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1answer
58 views

Graphing an ellipse on TI-nspire CX CAS

How do I graph an ellipse on a TI-nspire CX CAS? I know how to graph an ellipse with the equation $$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2 }=1$$ but I don't know how to put coefficients in the ...
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2answers
47 views

Conic Sections - Why do I need to know all these terms (foci, latus rectum, directrix, etc)? When will I use them?

I believe in learning something because I want to. If I do not want to learn about a subject or concept, I will not learn it well and master it. I am currently learning about conic sections, and I am ...
3
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0answers
54 views

Quadric question

I'm trying to prove that given 3 disjoint lines in $\mathbb{P}^{3}$ there exists a non-singular quadric containing them. The exercise is from the following link: ...
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0answers
22 views

Parabolic regression with restricted shape

How can I calculate the parabolic regression with vertex at minimum. Is it possible? I have a set of points from which I estimate the parabola using the (I believe) standard equation (from ...
0
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1answer
32 views

3D Graphing--finding an equation given a graph

I'm having trouble finding a reasonable equation for this graph: http://i58.tinypic.com/15gtrn7.png The x axis is the horizontal, y-axis is the axis coming out of the screen, the z-axis is vertical. ...
0
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1answer
26 views

How do you find an equation for a locus?

Part 1 Given a directrix at x=-8 and a focus point at (-2,0), what are 5 points where the distance to the directrix is twice as far as the distance to the focus? Example: (4,0) is one of the 5 ...
3
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1answer
33 views

Regular division of the perimeter of an ellipse

I would like to divide an ellipse into $N$ parts such that these $N$ parts have the same arc length. So given let's say $a$ and $b$ the semi-axis of an ellipse centered on $(0,0)$ and a positive ...
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3answers
309 views

Parabolic word problem

A rectangular barge is traveling under a bridge with a parabolic archway. The barge is 60 feet tall and 80 feet wide. The bridge is 80 feet tall and 200 feet wide. If the barge must travel down the ...
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1answer
42 views

Finding a hyperbola's equation based off given asymptotes

I need help finding the equation of a hyperbola that opens vertically with asymptotes $y=2x+11$ and $y=-2x-1$. I also need help finding the equation of a different hyperbola that also opens upwards ...
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1answer
35 views

Longest parallel chord of an ellipse

I am searching for a source demonstrating that, for any set of parallel chords spanning an ellipse, the longest chord passes through the center of the ellipse. I am not referring to the major and ...
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1answer
28 views

Moving between different ellipse representations

I have a representation of an ellipse that is the affine transform of the unit ball, $\|Ax + b\| <= 1$. My question is, how can I change this ellipse representation? I would like to have it in ...
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1answer
65 views

What software should I use to graph this? / How do I get rearrange this equation so that it is in terms of y?

I thought I'd just quickly tell you guys why I want to graph this equation before giving it you. We're studying conic sections at the moment, and I started wondering what would happen if I let the ...
0
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1answer
17 views

How do I find the width of a given section of an ellipse?

How would I be able to find the width of a horizontal ellipse (with a major axis of 120 and a minor axis of 5) at any given point along the major axis?
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1answer
26 views

conics ellipse and circle

If $a$ and $c$ are positive real numbers and the ellipse $\frac{x^2}{4c^2} + \frac{y^2}{c^2} =1$ has four distinct points in common wt the circle $x^2+y^2=9a^2$ then a) $9ac-9a^2-2c^2 < 0$ b) ...
0
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1answer
51 views

Find the arc-length of the circle with radius a?

Find the arc-length of a circle with radius a. From the equation of a circle, I found out the equation for the one quadrant, which is: $y = \sqrt{a^2 - x^2}$ I tried solving the problem, and here's ...
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0answers
31 views

Conic equation from cone/plane intersection

In an orthonormal cartesian frame $(O; \vec{x}, \vec{y}, \vec{z})$ consider: an infinite plane $P$ defined by: a point $p = (p_x, p_y, pz)$ an normal vector $\vec{n} = (n_x, n_y, n_z)$ a cone $C$ ...