Ellipse Definition and 406 Threads

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 What is the expression for z (the height above the xy-plane) in terms of r,f,w,i. r = the distance f = the angle between the semi-major axis and the r vector w = the angle that the semi-major axis makes with the y-axis i = the angle that the plane of the ellipse makes...

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...

My equation is x^2+(y^2/4)=1 I need to find where it is centered. I thought that from the original ellipse equation ((x - h)^2 / a^2 + (y - k)^2 / b^2 = 1) that the center is at (h,k). But in the options for my answers, (o,o) is not available. Am i missing something here?

I tried using site, https://www.physicsforums.com/mathjax/test/preview.html but after putting in the codes and pressing enter, nothing happens. I will test by trying the code tags here: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 For reference, I used...

I have been spending a few days reviewing parts of College Algebra from College Algebra, by Aufmann, Barker, & Nation. I am following the discussion of the shape, features, and equation for an ellipse, and I understand the derivation well, EXCEPT that I do not know how the subsitution of b2 =...

Homework Statement Find the largest and shortest distance from origo to the ellipse. Homework Equations Ellipse: g(x, y) = 13x^2 + 13y^2 + 10xy = 72 Function to optimize: F(x, y) = \sqrt{x^2 + y^2} But this is easier to optimize: f(x, y) = x^2 + y^2 The Attempt at a Solution I set...

Homework Statement Find the average value of the positive y-coordinates of the ellipse x^2/a^2 + y^2/b^2 = 1 I don't know where to begin, please help.

Hello, So I'm doing some independent study and I'm at a loss for this problem. Homework Statement Let's say we have an ellipse of the form (x2)/a + (y2)/b = 1 which we obtain by slicing a plane through a right circular cone with an opening angle of \theta (a fixed constant). We know...

Hi everyone, As I wasn't able to find it within my calculus book, can someone master here please tell me is there any way to find the angle of ellipse? Thank you Huygen

Homework Statement First of all, I'm not sure the following is achievable at my level (last year of high school), as it is not posed as a direct question, but if yes, could you point me in the right direction? I'm trying to find an ellipse that goes through three points, (0,0) , (b,0) and...

Hi to everyone. I'm detecting collision between two ellipses. I've got my unit vector, my ellipse center and radius (horizontal and vertical). I want to calculate the point that lies in the ellipse on the direction of the unit vector. See the image attached. Suppose the red arrow is my unit...

Hey guys, this isn't a course work question more independent study to improve something I'm working on for my course, to increase computation time. It may be in the wrong thread but the others state to post independent study in the homework section so its here. Placed it in maths since its...

Can the semi - major and semi - minor axes of an ellipse be time dependent? More specifically, can you have time dependent semi - major and semi - minor axes present in the standard form of the ellipse? I have an equation of the form \frac{(\xi ^{1}(t))^{2} }{a^{2}} + \frac{(\xi...

Homework Statement If there is an an ellipse x^2/9 + y^2/16 = 1, and the slope of the tangent is dx/dy = -16x/9y, how do you find what points at which the slope of the tangent is 1? I have no idea how to answer this and I've been trying for like an hour. Can anyone help me? Homework...

If there is an an ellipse x^2/9 + y^2/16 = 1, and the slope of the tangent is dx/dy = -16x/9y, how do you find what points at which the slope of the tangent is 1? I have no idea how to answer this and I've been trying for like an hour. Can anyone help me?

Homework Statement Find the standard form of the equation of the ellipse with vertices (4,0) and (-2,0) and foci (3,0) and (-1,0). Homework Equations ((x-h)^2/a^2) + ((y-k)^2/b^2) = 1 c^2 = a^2 + b^2 The Attempt at a Solution I haven't got much of anything: (x)^2 / 8 I'm pretty...

Homework Statement x^2+4y^2-8y-6x+9 convert this equation to the standard form of an ellipse and identify the foci, the middle point, Homework Equations x^2/b^2+y^2/b^2 The Attempt at a Solution Ellipse-----> My standard form of this ellipse ((x-3)^2/(2)^2)+((y-2)^2/(1^2))-4 I...

I need to find whether or not a point is within an ellipse. The problem is that the ellipse is tilted at an angle and not at the origin. I've tried Googling everywhere and can't find a good equation for what I need. Does anybody know the formula for an ellipse that includes: 1. Coordinates...

Gday, This may be a trivial questiom, but I just cannot figure it out. Why is mechanical energy conserved with an elliptical orbit? I understand that the mechanical energy of the system, i.e. both bodies, is conserved, but how is this isolated to the satellite's mechanical energy being...

If I was solving an ellipse problem and I had b^2 = (5/3) wouldn't that be simplified to + or - sqrt (15/3)? Or would it just be + or - sqrt (5/3)?

For an object in an elliptical orbit around the moon, the points in the orbit that are closest to and farthest from the center of the moon are called perilune and apolune, respectively. These are the vertices of the orbit. The center of the moon is at one focus of the orbit. A spacecraft was...

find the equation of an ellipse whose foci is (0,4)? Im not really sure of how to begin with this. Its actually a graph problem and it only gives the foci. can someone help me with this?

Hello. This is 2D with arbitrary orientations. I have a quadratic curve segment defined by 2 end points and another one in between. I can find lots of other points along this curve. I want to find a close-enough elliptic spline. It is defined by 2 end points and the point of intersection...

I have been scouring the Internet and various geometry books trying to figure out an issue I'm dealing with at work (I'm a professional statistician). It's been over 30 years since I've had a geometry class, so my brain is a bit rusty in this area. Here's what I have so far, can someone tell...

Homework Statement So here's a question from my textbook 'Calculus: Concepts and Contexts' 2nd ed. by James Stewart. This is section 3.6 # 54 We have Cartesian coordinates set up with an ellipse at x^2 + 4y^2 = 5 To the right of the ellipse a lamppost (in 2D!) stands at x=3 with...

How do you approximate the ellipse of an object's orbit using Newton's law of universal gravitation? I'm working on a 2D space game and that's pretty much the only physics I use, so no other forces to consider.

I need help with example 5.4L. I can understand all the working steps but i don't understand how they get m1 and m2, which is the point of intersection of the two perpendicular tangent... Can anyone enlighten me?

If you parameterize an ellipse such that x=acos(t) and y=bsin(t), then you quite easily get the relations: r={acost, bsint} v={-asint, bcost} a={-acost, -bsint} But my issue is that now, if I think of the equations as representing the motion of a planet about its sun, the acceleration...

Homework Statement I have an orbital mechanics problem, in which I need to find the area of the ellipse from pericenter to pi/2 (semi-latus rectum location). Homework Equations So I have the orbit equation r = p/(1+e*cos(theta)) where the origin is at the focus. So I know that A...

Hi there. have been looking at the problem: given that r=\frac{a(1-e^2)}{1+e\cos\theta} where: r is the distance from one Focus F to a point on the ellipse a is semi minor axis e is eccentricity \theta is angle (going anti-clockwise) from the focus F show that A=\pi ab where...

Hi, I'm trying to write a C program to build an ellipse given 3 points and the focus equals to (0,0); can someone help me out? Regards, CPtolemy

Homework Statement Determine the integral of f(x,y)=xy over x^2 - xy + 2y^2 = 1 in terms of an integral over the unit circle. Homework Equations The Attempt at a Solution The associated hint is to complete the square (which I did...and got messy expressions for x and y). I would...

Equation for Ellipse from a chord -- no other parameters! Homework Statement Known conditions are: End points of the chord intersect the major and minor axis. Proximity to nearest parallel tangent. Known (hypothetical) values are: The length of the chord is 10. The chord is 1.25 from...

How does the function f(z) = z + 1/z take a circle of radius g.t. 1 to an ellipse? How do I think about it geometrically ? (i.e., how should I be able to look at the complex function and tell straight away)

Homework Statement As I was relearning some concepts in calculus, I came across a section on ellipses. What I don't understand is why a and b in the standard equation of an ellipse govern the length of the minor/major axes. Can anyone shed some light? Thank you very much! Homework...

If so, can I get a hint on how to do it? I did a text search for a proof in "Conics" by Apollonius, but couldn't find one. If they couldn't prove it without calculus it means they had to wait until at least Newton's time to find the area of an ellipse?

Homework Statement try ∫∫G x^2 dA ;value is the region bounded by the ellipse 9x^2+4y^2=36 Homework Equations The Attempt at a Solution i think i have to change the variables to polar coordinate or U,V function but i have no idea.

Draw an ellipse. Then draw a curve that is equidistant all the way around the outside of the ellipse. Is that new curve also an ellipse? I've drawn it out and I can show examples where it's obviously not an ellipse, but I can't come up with a good non-visual explanation. I thought that maybe...

Potential Flow Field around an Ellipse** Ey guys Just wondering if anyone knows of any theory's that can be used to create a potential field around an ellipse in non uniform flow? I would have used a full Rankine body, but that requires uniform flow so it won't work in non uniform flow...

Parabola or an ellipse?? Homework Statement I have a curved structure which looks like this: http://imageupload.org/pt-1412920046522.html I haven't been told specifically what it is. I assumed it to be ½ellipse. It has a height of 36m. So, I also found out the equation y=...

Homework Statement Consider the curve x^2+xy+y^2=27 Homework Equations Find all points on the curve where the lines tangent to the curve are vertical The Attempt at a Solution I found dy/dy = (-2x-y)/x+2y) and I think I found the equations of lines visually to be x=6 and x=-6...

Hi. I know about the general formula for an ellipse: x^2/a^2 + y^2/b^2 = 1, that can be used to isolate y and calculate x,y points in excel. That's great, so far so good. That will create a ellipse, with horizontal A (x) axis and vertical B (y) axis. But what if one wants to rotate the...

Find the area of the largest rectangle that can be inscribed (with sides parallel to the axes in the ellipse). x^2/a^2 +y^2/b^2 = 1 I came across the above problem and am not sure how to proceed with it. I drew the ellipse with the inscribed rectangle and tried repositioning the ellipse so...

I have been struggling for a while now with this one. Lets say I have two points on the arc of the ellipse. I know the y-coordinates and the difference of the x-coordinates. Is it possible two calculate the equation or the semiaxes of the ellipse where these points are located? These are the...

I have been struggling for a while now with this one. Homework Statement Let's say I have two points on the arc of the ellipse. I know the y-coordinates and the difference of the x-coordinates. Is it possible two calculate the equation or the semiaxes of the ellipse where these points are...

Homework Statement I have the following: x(t) = acos(kt) + bsin(kt) y(t) = aksin(kt) + bkcos(kt) The Attempt at a Solution I'd like to show this is an ellipse, by actually explicitly finding the equation, but I honestly I have no clue about how to do this. Wiki gives the equation of an...

Homework Statement Ellipse with vertex at (2,3) and (-4,3) and focus at (1,3) Homework Equations (x-h)2/a2 + (y-k)2/b2=1 The Attempt at a Solution (h,k)= (-1,3) a2=9 (x+1)2/ b2 + (y-3)2/ 92

What is the condition for a hyperbola and an ellipse to intersect orthogonally? I have a formula for orthogonal circles -> 2g1g2 + 2f1f2 - c1c2 = 0