Ellipse Definition and 406 Threads

Homework Statement A body with mass ##m## can move without any friction on ellipse that ##(x/a)^2+(y/b)^2=1## describe. In ##y## direction homogeneous gravity field ##g## is present. For generalized coordinate we take angle ##\alpha ## defined with ##x=acos\alpha ##, ##y=bsin\alpha ##. Find...

Homework Statement Find the magnetic field due to a curved wire segment. Homework Equations Biot-Savart Law (differential form) dB=\frac{\mu_{o}i}{4\pi} \frac{d\vec{S}\times \hat{r}}{r^{2}} The Attempt at a Solution In class we found the magnetic field at a point in space (point P) caused by...

If you are looking at the upper right quadrant of an ellipse centered at (0,0), with a=1 and b=.6, and there is a 45 degree line drawn from (1,.6), how would I find the (x,y) coordinate where the line crosses the ellipse? (I have been out of school for a long time, this is not homework).

Hi, does exist an easy way to change the center of circle or a ellipse in polar coordinates? thanks!

Homework Statement Simplify sqrt(x^2+(y-sqrt(5))^2) = 8 - sqrt(x^2 + (y+sqrt(5))^2) The Attempt at a Solution I know squaring both sides, collecting like terms and simplifying gets the equation but in my solution manual they do it a different way that is a lot shorter and I need help...

Calculate the length of the axes of the ellipse's area minimum that can be confined to a rectangle of sides: 2p and 2q answer Sqrt 2p Sqrt 2q I have just solved it

Homework Statement Given an electric field: E=Ex*ex+Ey*ey with Ex=cos(kx-wt) Ey=cos(kx-wt+e) where e is the phase difference Show that Ex^2 + Ey^2 - 2*Ex*Ey*cos(e) = ( sin(e) )^2 Homework Equations Ex=cos(kx-wt) Ey=cos(kx-wt+e) The Attempt at a Solution Was...

I am trying to find a matrix A such that $(1)$ can be written as $v^TAv=1$ where $v=(x, y)^T$. $(1)$: $$\left(\frac{x}{a_1}\right)^2 + \left(\frac{y}{a_2}\right)^2 - 2\left(\frac{xy}{a_1a_2}\right)\cos(\delta)=\sin^2(\delta)$$ $$a_1, a_2, \sin(\delta)\neq 0.$$ I am positive that $\cos(\delta)$...

Hi all, How should I divide quarter of an ellipse into two equal havles? At what angle should I divide so that the 2 parts are equal? Any hint is a privilege. Thanks in advance Regards Suji

Problem: Find the condition so that the line px+qy=r intersects the ellipse $\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ in points whose eccentric angles differ by $\frac{\pi}{4}$. Attempt: Let the points on ellipse be $(a\cos\theta,b\sin\theta)$ and...

I'm trying to find the equation of a general ellipse given 3 points. Two of those points should be at each end of one axis. Using this I have the center of the ellipse, and the angle of rotation with respect to the x-axis that this axis is rotated. It's unknown whether this is the major or minor...

The centripetal acceleration of a circle is: a_c = \frac{v^2}{r} * u_n. The acceleration of an ellipse is different. It increases from from apoapsis to periapsis as the position changes from furthest point in the orbit to the closest. Then decreases from from periapsis to apoapsis as the...

Homework Statement Find the equation of the tangent, and the line which passes through the origin to the point where x= 3/2 4x2+9y2 = 36Homework Equations The Attempt at a Solution Using implicit differentiation d/dy [4x2+9y2] =36 8x+18y dy/dx = 0 dy/dx = -8x/18y Coordinates are (1.5...

What is the radius of curvature formula for an ellipse at slope = 1? I have found b^2/a, and a^2/b for the major and minor axis, but nothing for slope = 1. Thanks.

I'm doing this in Matlab but it's not restricted to any particular software. I have a bunch of geographical points (x,y coordinates for each) and I want to take all the points that are 50 km or closer to the reference point. I took the great-circle equation to convert geographical longitude...

A surface is obtained by rotating around the x-axis the arc over the integral(-1,0.5) of an ellipse given by: x^2+4y^2=1 What is its surface area? Here's my solution: I use the equation: S=integral( upper bound: a lower bound: b ) 2(pi)y*[1+(f'(x))^2]^0.5 dx Since x^2+4y^2=1...

Homework Statement The question simply states that the focals are (0,2) and (2,-1) and I need to form an equation from it. I know that in complex form this would be |z-(0-2i)| + |z-(-2+i)| or more simply |z+2i|+|z+2-i|. Is this right?

Hello =] I'm having trouble with this question, can somebody please help me with it! I'll thanks/like your comment if help me =) ![Question][1] I know that for a ellipse the parametric is x=a sin t , b= b cos t t:0 to 2pi (?) for part a) I drew up the graph but not sure if it's...

hello! I have to verify the formula of the moment of inertia of an ellipse about its' centroidal axis, is it M*(a^2 + b^2)/4.This is the one I got by myself. But in a webpage it was given as Pi*a*(b^3)/4. NOTE: don't ask for the proof of what I did.Its' a bit longer.I just want to know...

Homework Statement Find the equation for the conic ellipse with vertices (-2,-5) (-2, 4) and foci (-2,-4) (-2,3) Homework Equations I want to make sure I am solving the problem correctly The Attempt at a Solution (x+2)^2/8 + (y+0.5)^2/20.25 =1

Find the ellipse centered at the origin that runs through the points (1,2), (2,2), and (3, I). Write your equation in the form $$ ax^2 + bxy + cy^2 = 1 $$ I understand the $$ ax^2 $$ and $$ cy^2 $$ in the equation because the equation of an ellipse centered at origin is $$ (x/a)^2 + (y/b)^2 = 1...

Homework Statement 7 Find the points on the ellipse x^2 + 2y^2 = 1 where the tangent line has slope 1 Homework Equations The Attempt at a Solution I got the correct X and Y values but this gives me four possibilities and the answer key says there are two points. I got x...

Homework Statement If P and Q are two points on ellipse [(x^2/a^2)+(y^2/b^2)]=1 such that PQ subtends a right angle at the centre O then.Prove that 1/[(OP)^2] + 1/[(OQ)^2] = [1/(a^2)] +[1/(b^2)] Homework Equations Parametric form of points P(acos(θ),bsin(θ))...

Homework Statement Find parameter a so that line y=ax + 11 touches ellipse 3x^2 + 2y^2 = 11 The Attempt at a Solution| I can rewrite ellipse equation like \frac{x^2}{\frac{11}{3}} + \frac{y^2}{\frac{11}{2}} = 1 And i know that line y=kx + n touches ellipse when a^2k^2 + b^2 = n^2...

Homework Statement i'm having trouble with these solid of revolution problems because a lot of them require you to find "length of the segment" before evaluating the problem. example: a solid lies between planes perpendicular to x=-5 and x=5. the cross section in the xy plane is the ellipse...

To find the area, you break the ellipse into infinitesimaly small triangles and integrate. But why? Why not break it up into infinitesimaly small circle segments and calculate it through circumference instead? There are other problems regarding integration of geometric objects that has me...

I was wondering about how to find the circumference of an ellipse. I googled for it and found this: http://paulbourke.net/geometry/ellipsecirc/ That got me pretty amazed! I don't know high level maths, but still, can someone please explain to me why the circumference takes such a complicated...

I drew an ellipse and then bisected it with a line with the basic \draw. How can I color/shade from the line to the ellipse boarder? We can't use \filldraw () -- () arc ( : : radius) since the radius of an ellipse changes.

Hi, I'm trying to find \iint_S \sqrt{1-\left(\frac{x}{a}\right)^2 -\left(\frac{y}{b}\right)^2} dS where S is the surface of an ellipse with boundary given by \left(\frac{x}{a}\right)^2+\left(\frac{y}{b}\right)^2 = 1 . Any suggestions are appreciated! Thanks, Nick

An ellipse has the equation x^2+5y^2=5 a line has the equation y=mx+c a) show that if the line is a tangent to the ellipse then c^2=5m^2+1 b) hence find the equation of the tangent parallel to the line x-2y+1=0 I tried to find the gradient of x^2+5y^2=5 at a point (x1,y1) and then put it...

Hi, Given that the flow normal to a thin disk or radius r is given by \phi = -\frac{2rU}{\pi}\sqrt{1-\frac{x^2+y^2}{r^2}} where U is the speed of the flow normal to the disk, find the flow normal to an ellipse of major axis a and minor axis b. I can only find the answer in the...

I can do this calculation using different methods; my interest is improving my skills at using this method, rather than the answer. Trying to find the area of the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 From the Jacobian, we get dxdy = rdrd\theta So I go from the above equation of the...

This is really a simplification of an equation. It is just very long and complex and I need advice. For ellipse center at the origin with tilt angle \tau, the distance from origin to the ellipse is \rho(\varsigma). It is given: \varsigma\;=\;\frac...

An ellipse is represented by \rho(t)^2=x^2(t) + y^2(t) where \rho(t) is the distance from origin to the ellipse at a given time. The way the article used to find the major and minor axis is the take the derivative \frac{d(\rho^2(t))}{d t}=0 to find the maximum and minimum. My question is why...

Homework Statement A point is chosen randomly in the interior of an ellipse: (x/a)^2 + (y/b)^2 = 1 Find the marginal densities of the X and Y coordinates of the points. Homework Equations NA The Attempt at a Solution So this ought to be uniformly distributed, thus the density function...

Here is the question: Here is a link to the question: Tangent line to a ellipse? - Yahoo! Answers

1) If we have the focus as (f,g) and the directrix as Ax+By+C =0 and the eccentricity as e we define the equation of the ellipse to be (x-f)2+(y-g)2 = e2(Ax+By+C)2 / A2+B2 Does this imply that the variables x and y in the locus of the directrix and the ellipse refer to the same thing?(we...

Homework Statement Write the equation of the conic that meets the conditions: An ellipse that has the centre at (0, 0), has a horizontal major axis, the eccentricity is 1/2 and 2c = 1.Homework Equations \frac{(x - h)^2} {a^2} + \frac{(y - k)^2}{b^2} = 1 The Attempt at a Solution 2c =...

I'm a collage teacher and I've found a very hard problem in one of my math classrooms' textbooks. It was firstly proposed as problem n. 9, back in 1995, in the "Annual Iowa Collegiate Mathematics Competition". Link is here (no solution file available in the site for that year). The text is...

\vec E\;=\; \hat x E_{x0}\cos(\omega {t} -kz)\;+\;\hat y E_{y0}\cos(\omega{t}-kz+\delta) For z=0, this is a vector that trace out an ellipse with time t. I want to 1) to verify that using the definition of differential calculus, we can find the length of the major and minor axis by...

Homework Statement The angle between the tangents drawn from the point (2,2) to the ellipse, 3x2+5y2=15 is: a)##\pi##/6 b)##\pi##/4 c)##\pi##/3 d)##\pi##/2 Homework Equations The Attempt at a Solution To find the equation of tangents, I need to use the following formula...

how to calculate the double integral of f(x,y) within the intersected area? f(x,y)=a0+a1y+a2x+a3xy The area is the intersection of an ellipse and a circle. Any help will be appreciated, I don't know how to do this. can I use x=racosθ,y=rbsinθ to transformer the ellipse and...

Hello, I am tasked with plotting the polarization state of a laser (basically I've made a polarimeter), but I really have no idea where to go at this point. Below is a sample of the program I have written with some real data that I just took from a laser. I have the intensity profile as a...

Homework Statement PM and PN are perpendiculars upon the axes from any point 'P' on the ellipse. Prove that MN is always normal to a fixed concentric ellipse Homework Equations The Attempt at a Solution I assume point P to be (acosθ, bsinθ) The eqn of line MN is then given by...

Homework Statement The tangent at any point P of a circle meets the tangent at a fixed point A in T, and T is joined to B, the other end of diameter through A. Prove that the locus of point of intersection of AP and BT is an ellipse whose eccentricity is 1/ \sqrt{2} Homework Equations...

Homework Statement Prove that a variable chord of ellipse which subtends 90° at the centre is always tangent to a concentric circle Homework Equations The Attempt at a Solution I assume the simplest equation of ellipse to be \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1 and the variable chord...

Homework Statement A bridge is to be constructed across a river that is 150 feet wide. The arch of the bridge is to be semi-elliptical and must be constructed so that a ship less than 50 feet wide and 40 feet high can pass safely through the arch, as shown in the figure. (a) Find an equation...

Hi All, I'm not a math guy so I am coming to you for help. I am trying to come up with an equation to graph any 180 degree curve that is comprised of: a 135 degree radius, and a 45 degree ellipse (135 + 45 = 180). The two curves being the same curvature (slope?) where they meet. The portion...

Homework Statement Homework Equations Lagrance Multipliers. The Attempt at a Solution This is a pretty dumb question, and I feel a little embarassed asking but.. I know how to do the Lagrange part (I think). I'm assuming you maximize/minimize the distance, \sqrt{x^{2} +...

Homework Statement Let k>0 be such that (x^2-x)+k(y^2-y)=0 defines an ellipse with focal length equal to 2 . If (p,q) are the coordinates of a point in the ellipse with q^2 - q\not=0 , then what is \frac{p-p^2}{q^2-q} ? Homework Equations The fact that the sum of the distances from...