Ellipse Definition and 399 Threads

How do you calculate the Normal vector to an Ellipse. Radius Vector: r=rx*i + ry*j + rz*k Velocity Vector: v=vx*i + vy*j + vz*k at this point I would like to calculate the Normal to the ellipse. That is as far as I been able to calculate. Any help or suggestions are welcome.

Sketch the following region: | z+i | + | z-1 | =2 I know that it is a ellipse, but i am trying to replace the z for x +iy. I reached the following equation. 3x^2+3y^2 = 4x-4y+2xy now how can a simplify it in order to have the ellipse equation: (x^2/a^2) + (y^2/b^2) = 1

Can an ellipse's focal points be outside the ellipse? I have tried googling this, but without any good explanations or answers. According to my calculations, the focal points of the ellipse defined by x^{2} + \frac{y^{2}}{4} = 1 are (-\sqrt{3},0) (\sqrt{3},0)) . I maybe wrong of course...

I don't know what category this question falls into. I have two parallel planes, on one I draw a circle and on the other I project it orthogonally. Now I incline the plane with the circle. The projection on the other plane will be an ellipse. I need to find out, the relationship between the...

1. Deriving the major and minor axis of an ellipse from conjugate diameters pointsCurrent solution: double x1 = Diameter1.X - Center.X; double y1 = Diameter1.Y - Center.Y; double x2 = Diameter2.X - Center.X; double y2 = Diameter2.Y - Center.Y; double xc = (x2 + y1) / 2; double yc = (y2 - x1) /...

Homework Statement Find the equations of the osculating circles of the ellipse 9x^2 + 4y^2 =36 at the points (2,0) and (0,3) Homework Equations The Attempt at a Solution I honestly have no idea what to do here. This problem is in the chapter relating to curvature and arc length...

Hi, dear all, hope your guys allow me to ask this tricky question. Refer to the attachment, i would like to derive the principal radii of an ellipse, the final equation and figure is provided in Stephen Timoshenko Theory of plates and shells 2nd edition. consider the ellipse has form...

Homework Statement Within the xy-plane, two vectors having lengths P and Q rotate around the z-axis with angular velocities ω and –ω. At t = 0,these vectors have orientations with respect to the x-axis specified by θ1 and θ2. How do I find the orientation of the major axis of the resulting...

In a game I'm developing, I have an ellipse which contains a blue shape inside of it like follows: http://img6.imageshack.us/img6/9518/screenshot20120815at938.png In the picture, the curves of the blue shape have the exact same arc as the area of the ellipse that it mirrors. In this...

Suppose I have a vector space. There is circle with center at the origin of the vector space. There is also a line L going through the origin at some angle. On the circle is a point moving around the circle at a constant speed. The vector from the center to the point makes some angle with...

I know I should keeps this short, but I need to explain it a little. So, please have patience with me :) Given a standard ellipse, and its eccentricity and position on screen, is there some clever way of calculating how much a regular circle needs to be tilted in (angles) in a perspective...

Homework Statement Points are A(-6,2) and B(-3,4) and ellipse 4x^2 + 9y^2 = 72. Point C(x,y) for which triangle ABC has largest area is? Homework Equations Ellipse equations The Attempt at a Solution I don't know even where to start. As far as i am concerned that point can be any...

I've got a nifty java program done which calculates the orbit of a body around a gravity source. The math and physics are all done for a body around a single gravity source and how to figure whether it's an ellipse, parabola, hyperbola or straight line. But now I've got a new problem. If...

Homework Statement Find the area swept out by the line from the origin to the ellipse x=acos(t) y=asin(t) as t varies from 0 to t_{0} where t_{0} is a constant between 0 and 2\pi Homework Equations The Attempt at a Solution so using Greens Theorem in reverse i get A=\frac{1}{2}\oint_{c}...

What does it mean when one says that "A circle and an ellipse with a focus at the circle’s center can touch each other only at the longer axis"? Can't you, by varying the size of the circle, make it intersect the ellipse in a variety of ways? Thanks! :)

I'm trying to find the polar equation first, and I learned this today but I forgot a lot of it and we're not allowed to take notes in class (professor says it helps to learn better) so I'm trying to look it up online but it's not much help because I can't find any elementary lessons on polar...

Hello! I'm not sure this is the right place to ask, but i have a huge problem. I have an axis and it's origin, and also a point. I suposed that is enought to describe an ellipse, but how to do so? I want to describe it by having it's center and both it's radius. Some images to ilustrate what I...

Given a bivariate gaussian distribution, I'm attempting to find the probability p for which the ellipse of all points (x,y) for which P(X = x, Y= y) = p contains a given % of the samples drawn from the distribution. I want the 2d equivalent for the 1 dimensional case: given a normal...

Homework Statement a elliptic paraboloid is x^2/a^2+y^2/b^2<=(h-z)/h, 0<=z<=h, show that the horizontal cross-section at height z, is an ellipse Homework Equations The Attempt at a Solution i don't know how to prove this, i only know that the standard ellipse is...

Homework Statement Given the vector (6,-15) and foci (6,10) (6,-14), Find the equation of the conic.Homework Equations Vector = <6,-15> (x-h)2/a2 + (y-k)2/b2 = 1 Foci (h+c,k) and (h-c,k) vertices (h+a,k), (h-a,k) The Attempt at a Solution k = 6 h=-2 a=-12 I'm not sure what I'm doing. How do...

Here is the simple question. When I differentiate the area of a circle, I got the parameter. As the Area is the sum of Circumference. But why cannot I get the circumference of ellipse by differentiate the area with respect to the radius (I set it as the longer side). The answer I got is...

Homework Statement Find the arc length of the ellipse or deformed circle. r^2=x^2+(y/β)^2 r=radius β=dilation constant k="random" constant Homework Equations The Attempt at a Solution I suspect it's impossible but I can't prove that. After working it out I got stuck with these...

Greetings everyone, I am having difficulties grasping the polar form of the ellipse equation, and there seems to be more than one way to express an ellipse in this form, if I am not mistaken. For example on the following webpage http://farside.ph.utexas.edu/teaching/301/lectures/node155.html...

Hi, Concerning only the upper right quadrant of an ellipse... I know the distance from the center of the ellipse to the top of the ellipse, (semi-minor axis "b"), is 1000. I know the distance from the center of the ellipse to the side of the ellipse, (semi-major axis "a") is 1732. At the...

Homework Statement The point P on a circle is transformed into the point P' on a ellipse. The point P is (6,8), and lies on a circle with the equation X^2 + Y^2 = 100. Point P' lies on the same graph after it has been transformed into a ellipse, with the co-ordinates (4,12). (No...

Homework Statement An art museum worker leaves an 8-foot-tall painting leaning against a wall. Later, the top of that painting slides down the wall, and the painting falls to the floor. Use the diagram to find an equation of the path of the point (x,y) as the painting falls. Homework...

I need to move an object based on 100 images rotating. The object needs to move in a path that is forming an ellipse when I'm rotating the image based on my gestures. I have 4 points, 2 pairs of opposite points on X/Y axis, on the ellipse but how do I calculate the rest of the points so that...

all of my work so far is in the picture. I'm stuck on what i should do next.

Homework Statement Find equations of both the tangent lines to the ellipse x2 + 4y2 = 36 that pass through the point (12, 3). Homework Equations The equation of an ellipse is x2/a2 + y2/b2 = 1. I converted the given equation to x2/36 + y2/9 = 1 by dividing each value by 36. The...

Hope this is in the right forum. I apologize in advance for my ignorance and imprecise discussion as I am at a major disadvantage, lacking rich mathematical educational background enjoyed by most here. Background is that I'm curious about calibrating for soft-iron distortion calibration for a...

Homework Statement Prove that the equations x=acos(\theta) and y=bcos(\theta +\delta ) is the equation of an ellipse and what angle does this ellipse's major axis make with the x axis? Homework Equations Equation of an ellipse is x=acos\theta, y=asin\theta Rotation matrix is for a rotation...

Hello, I'm having a problem finding the minor and major axsis lengths of an ellipse from three points, the ellipse's center, and two conjugate end point diameters. I have no problem solving the problem when the conjugate diameters align with the minor and major axsis, but when they don't the...

Hi everyone. I hope I've found the right place for my first post here. I have a geometry problem which I need to solve for a piece of software I'm writing, and I'm hoping someone might be able to help me. I have a non-rotated ellipse inside a circle, as in this diagram. I know the x and y...

Homework Statement Set up the integral for the area of the ellipse: \frac{x^2}{a^2} =\frac{y^2}{b^2} \le 1 in polar coordinates. Homework Equations maybe \int_\alpha^\beta \int_a^b f(rcos\theta , rsin \theta ) r \; dr \; d\theta or more likely \int_a^b \frac{1}{2} r^2 \; d\theta The...

Homework Statement Find parametric equation for (((x-2)^2)/4)+(((y+1)^2)/9)=1 Homework Equations ((x^2)/(a^2))+((y^2)/(b^2))=1 (ellipse equation)The Attempt at a Solution I tried solving for y which gave me y=(6/(x-2))-1, but that did not work.

Where did I go wrong? I showed all my work in the paint document... My thought is that I am using the incorrect approx rec and I am guessing that it extends into both the first and second quad, and not just the first quad, as I indicated in my picture.

In the equation \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 can someone explain what those a and b are doing? I know they are the x and y intercepts of the graph, but why are we dividing x^2 and y^2 by them? Also, why are they squared? Why not just regular "a" and "b" like in the parabola equation...

Hello to everyone! I am really desparately trying to find the length of the "radius" of an ellipse.I will explain exactly what I mean by that - its the length of the line segment that connects the center of a particular ellipse with a given point of the same ellipse.All the information I have...

Spot the error: The circumference of an ellipse with semi-major axis = 2 and semi-minor axis = 1 (i.e. \left( \frac{x}{2} \right)^2 + y^2 = 1 ) is 4 \pi. Proof: \textrm{circumference} = \iint_{\mathbb R^2}{ \delta \left( \left( \frac{x}{2} \right)^2 + y^2 - 1 \right) } \mathrm d x \mathrm...

Hi, guys, Is the ellipse equation "x=acost; y=bcost" a Cartesian coordinates equation or a polar coordinates equation? Someone said that it's a transfer from a polar one to a Cartesian one. Need more help on this, thank you very much!

Homework Statement The ellipse 18x^2+2x+y^2=1 has its center at the point (b,c) where b=____ and c=____? Homework Equations x^2/a^2 + y^2/b^2 = 1 The Attempt at a Solution 18x^2+2x+y^2=1 18(x^2+(1/9)x)+y^2=1 18(x^2+(1/9)x+(1/324))+y^2= 1+18(1/324) 18(x+(1/18))^2+y^2=19/18...

Homework Statement Evaluate. ∫∫D x2 dAxy, bounded by 5x2 + 4xy + y2 = 1 Homework Equations ∫∫D H(x,y) dAxy = ∫∫D H(u,v)\frac{\delta(x,y)}{\delta(u,v)}dAuv The Attempt at a Solution So I understand I'm supposed to find a change of variables to transform the ellipse into a circle...

Homework Statement If u=x^3 + 3xy + y^3, determine du/dx on the ellipse 2x^2+3y^2=1 2. The attempt at a solution Imagine I just use partial derivative somehow, but I'm not sure what the question is asking by on the ellipse. I have a feeling its just something simple that I'm...

Homework Statement Use Green's theorem to find the integral ∫C (y^2dx+xdy) when C is the following curve (taken counterclockwise): the ellipse x^2/a^2 + y^2/b^2 =1.Homework Equations Green's theorem: ∫C Mdx+Ndy = ∫∫R (∂N/∂x-∂M/∂y)dA The Attempt at a Solution I tried parametrizing the ellipse as...

How do I find the two tangent points of two lines from (0,0) to an ellipse? We have 2 equations, a general ellipse and it differentiated: 1: A*x*x+B*x*y+C*y*y+D*x+E*y+F=0 is an ellipse if B*B-4*A*C<0. Differentiating, 2: 2*A*x+B*x*dy/dx+B*y+2*C*y*dy/dx+D+E*dy/dx=0. If F<0, ellipse not...

Homework Statement Consider the PDE xu_x + y u_y = 4 u, -\infty < x < \infty, -\infty < y < \infty. Find an explicit solution that satisfies u = 1 on the ellipse 4x^2 + y^2 = 1. Homework Equations The Attempt at a Solution The characteristic curves are x(t,s) = f_1(s) e^t...

Homework Statement I did this one before a few weeks ago but now I can't seem to get the right answer: An elliptical disk is to fit snuggly and squarely into a notch cut into a rectangular plate. The notch is 180 mm wide. If the disk's major axis is 280 mm long and is parallel to the long...

I have an ellipse. Quite simple, ecc=0.60. And I'm doodling with calculus I learned 40 years ago. I can find the tangent to the ellipse, that is, the slope of the tangent, using cartestian coordinates. At the point where the tangent skims the top of the minor axis (b) the slope is 0 and and...

Homework Statement i need to draw an ellipse with a circumference of 59cm and a minor axis of 12cm. does anyone know how to draw one using the piece-of-string-looped-over-two-nails method, ie how long would the string need to be & how far apart should the nails be? i'll also need to know the...

I have been toying with a java programming project for a few months now. I want to depict a satelite orbiting a planet (2 dimensional). I've scaled down certain constants to fit the screen and have put GM (mu) at 200000 and the distance from the gravitaional body, a planet, at 200...