Ellipse Definition and 406 Threads

Hi, I have to resample images taken from camera, whose target is a spherical object, onto a regular grid of 2 spherical coordinates: the polar and azimutal angles (θ, Φ). For best accuracy, I need to be aware of, and visualise, the "footprints" of the small angle differences onto the original...

Homework Statement [/B] The tangent and the normal at a point P(3\sqrt2\cos\theta,3\sin\theta)) on the ellipse \frac{x^2}{18}+\frac{y^2}{9}=1 meet the y-axis at T and N respectively. If O is the origin, prove that OT.TN is independent of the position P. Find the coordinates of X, the centre of...

I'm given that: S is the surface z =√(x² + y²) and (x − 2)² + 4y² ≤ 1 I tried parametrizing it using polar coordinates setting x = 2 + rcos(θ) y = 2rsin(θ) 0≤θ≤2π, 0≤r≤1 But I'm not getting the ellipse that the original equation for the domain describes So far I've tried dividing everything...

Homework Statement It is given that the line y= mx + c is a tangent to the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2}=1 if a^2m^2=c^2-b^2 Show that if the line y=mx+c passes through the point (5/4, 5) and is tangent to the ellipse 8x^2+3y^2=35, then c = 35/3 or 35/9 Homework EquationsThe...

Homework Statement The ellipse is given as (x^2/a^2) + (y^2/b^2)=1 I´m meant to calculate a tangential vector, a normal vector and find an equation for the tangent using a random point (x0,y0). I´m meant to do this in 2 ways: firstly by using the parametrization x(t)=a*cos(t) and...

I posted a question about this yesterday, but realized I had made a stupid mistake in my derivation. Orbital dynamics: "The familiar arc-cosine form" That error has been corrected. I still have a deeper question. I believe this expression can be developed using the geometry of an ellipse in...

I have a real doosy that has got me stumped. I need to solve the following equation for v: tan(v + ω) = tan(θ + Ω)sec(i) The symbols stand for the following values in an elliptical orbit of one point source around another (on the celestial sphere): where v = true anomaly; ω = argument of...

1. Homework Statement The following question is posed within a section of my A level maths book titled "The Hyperbola" A set of points is such that each point is three times as far from the y-axis as it is from the point (4,0). Find the equation of the locus of P and sketch the locus 2...

Hello! Okay- This is a relatively simple problem, but for some reason I'm having huge difficulty with it. So I have the equation of an ellipse, x^2-6sqrt3 * xy + 7y^2 =16, which I have converted into quadratic form to get (13, -3sqrt3, -sqrt3, 7) and I need to rotate it using the normal...

I want to try and see the intersection between the hyperboloid and the 2-plane giving an ellipse. So far I have the following: I'm going to work with ##AdS_3## for simplicity which is the hyperboloid given by the surface (see eqn 10 in above notes for reason) ##X_0^2-X_1^2-X_2^2+X_3^2=L^2## If...

Hi PF I've beent rying to model the lunar orbit around the sun (cardioide) as a parametric function, but have run into a problem. f(t) = r(t) : x = a cos(ωt) y = b sin(ωt) z = k t The angular frequency ω as well as the distance from to the center varies around the orbit. Is...

I'm almost there in terms of understanding it, but I need to go beyond the text. Here is the example problem: imgur link: http://i.imgur.com/UMj55tF.jpg I can see that where we have 1 = \vec{x}^T A \vec{x} = \lambda \vec{x}^T \vec{x} that 1=\lambda \vec{x}^T \vec{x} = \lambda ||\vec{x}||^2...

Homework Statement 11) The tangent at P on the ellipse \frac{x^2}{a^2}+ \frac{y^2}{b^2}=1 meets the x and y axes at A and B. Find, in terms of the eccentric angle of P, the ratio of the lengths AP and BP. 12) Repeat Question 11 using the normal at P. Homework Equations bx \cos \theta + ay...

1. Problem: ellipse x^2/a^2 + y^2/b^2 = 1 encloses circle x^2 + y^2 = 2x. Find values of a and b that minimize the area of the ellipse.Homework Equations : [/B]A = pi*a*b for an ellipse.The Attempt at a Solution : [/B]I tried a bunch of crazy stuff... I know I need to find where the tangents...

I'm reading the professors notes and he gives this general equation for the ellipse. The professor has already been mistaken in some of his notes so I wanted you to help me validate what he's saying, as I can't prove the equation. Suppose we have the vector ##\mathbf{r}=\big(x_o \cos(-\omega t...

Find the equation of the ellipse whose eccentricity is 2/3 and which has (2,0) and x+y=0 for focus and corresponding directrix . given answer: (x-2)^2 + y^2 = 4/9 ( ( (x+y)/√2)^2)what i tried doing:- ae=2 ⇒a*2/3=2 ∴a=3 found b=√5. what to do next? please help.

Homework Statement For an ellipse, if we take the cross product of the velocity vector with the radial vector (distance from center of mass), it is equal to a constant h. Is this true? If so, what is the proof? Homework Equations n/a The Attempt at a Solution Conceptually it makes sense...

Homework Statement Consider the ellipse ##\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1## that encloses the circle ##x^{2}+y^{2}=2x##. Find the values of a and b that minimize the area of the ellipse. Homework Equations ##Area=ab\pi## The Attempt at a Solution I begin by completing the square...

So the formula for an ellipse in polar coordinates is r(θ) = p/(1+εcos(θ)). By evaluating L = ∫r(θ) dθ on the complex plane on a circle of circumference ε on the centered at the origin I obtained the equation L = (2π)/√(1-ε^2). Why then does Wikipedia say that the formula for the perimeter is...

Dear Friends! If we have a variable triangle formed by joining a point of ellipse and its two focii shown in figure,how to find locii of various centres.Can you please suggest some reference to find these .I have tried by using simple method for incentre locus which I left as it goes long...

I know that 1) when eccentricity is less than 1 then it is an ellipse 2) locus of points making sum of the distance from two fixed points(foci) with that point a constant, creates ellipse. Here comes the question, I understand that locus made according to number 2, is ellipsoidal. But how can...

Hi. Unfortunately, it looks like my first ever PhysicsForums post isn't even about Physics. I'll think of a Physics-related question later. :) Anyway, I know that each ellipse has an inscribed circle and a circumscribed circle, but I was wondering about a third circle associated with an...

I am trying to work out a formula for the approximate calculation of the lung capacity of a racehorse. http://performancegenetics.com/wp-content/uploads/2015/05/Horse.jpg I take three physical dimensions on the horse. 1) The measurement of the girth (which is the perimeter of an ellipse)...

Homework Statement Use the parametric equations of an ellipse, x = f(t)= a cos t and y = g(t) = b sin t, 0 <= t <= 2 pi, to find the area that it encloses.Homework Equations Integral for parametric equations. The Attempt at a Solution A = \int_0^{2 \pi} g(t) f^\prime(t) \; dt = \int_0^{2...

I have a paradox here. Look at this diagram of colliding ellipses (they might be elliptical prisms in 3D). Now if you stretch the image (for example looking at the image from an angle) it becomes two colliding circles. Therefore you would expect by that argument that the colliding force would...

Homework Statement Find the points on the ellipse 4x2+y2=4 that are furthest from the point (1,0) on the ellipse. Homework Equations Ellipse: y=±√(4-4x2) Distance Formula: d=√[(x2-x1)2+(y2-y1)2] The Attempt at a Solution The distance from (1,0) for any point on the ellipse should be...

This is a question I have been playing with this week out of curiosity but I keep coming up against brick walls and unenlightening results. Given the equation of an ellipse, say $$ x^{2} - xy + y^2 = 2, $$ I would like to find the equation of the line which passes through the major axis. I...

Homework Statement Homework Equations N/A The Attempt at a Solution Question 1) Suppose I tried to convert ##\int \int_c {-2y^3} dA## into polar coordinates. What would the limits be? I know that ##x = rcos(\theta), y = rsin(\theta)## but the two rs are different (unlike in a circle). Q2)...

Hello all, I'm calibrating a magnetometer sensor. An uncalibrated sensor will output values that will graph an ellipse. A calibrated sensor will output values that will graph a circle. Since there's data points all over the place, I'd like to find a piece of software that will take my data...

Homework Statement Find the curvature at the point (x, y) on the ellipse x^2/9+y^2/4=1. Homework Equations None. The Attempt at a Solution x^2/a^2+y^2/b^2=1 so I know that a=3 and b=2 for this problem. x(t)=acos(t) and y(t)=bsin(t) so x(t)=3cos(t) and y(t)=2sin(t) now what? What's the...

If a hyperbola passes through the focii of the ellipse x^2/25 +y^2/16 =1 and its transverse and conjugate axes coincide respectively with major and minor axes of the ellipse, and if the product of eccentricities of hyperbola and ellipse is 1, find the equation and focus of the hyperbola

Does anyone know how to find the area of an intersection between a cylinder of height 8 and radius 6 and a plane that passes through the cylinder, forming a chord of 10 units at the top and bottom faces of the cylinder? The area of intersection curves with the cylinder, forming a truncated...

Hey, sorry if this is not the right section to post in, the topic is a bit ambiguous. I've generated a set of coordinate points for the orbit of Mercury (3d cartesian) and now I want to fit an ellipse through it so I can get an accurate estimate of the location of the perihelion. I am using...

Homework Statement The Attempt at a Solution I thought that an ellipse shares vertices on the y-axis and the x-axis. Making it neither vertical major axis. I am unsure about the question.[/B]

The question is... So of course I rearrange my ellipse formula to get y=\pm\sqrt{1-\frac{{x}^{2}}{4}} Then I calculate my radius as x-(-2)=r \implies x+2=r I know the formula for finding volume with the Shell Method is V=\int_{a}^{b}2\pi x\cdot f(x) \,dx To make it easier I decide to just...

Homework Statement if the tangent at a point P("theta") on the ellipse 16 (x^2) + 11 (y^2) = 256 is also tangent to the circle (x^2) + (y^2) + 2(x) = 15 then ("theta") = ?? 2. The attempt at a solution {{{{ i have taken "theta" as "d" }}}} P [4 cos d , (16/(sqrt11)) sin d] equation of...

Write the equation for an ellipse with vertices (0,-3) and (0,3), minor axis of length 10. I know that the standard form of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2=1 Please help me ! Please! Thank you so much for your time, I appreciate it.

I was asked to look at a problem (not homework) in which a tangent ellipse is to be found for a circle. This puzzle is turning out to be more than I bargained for. See the attached image because hey, a picture's worth a thousand words. The givens in this problem are to be the radius ##R_i## of...

Homework Statement (This isn't coursework, just a revision question) Exercise: An ellipse can be defined as the locus of all points, P, in the plane such that PF_1+PF_2=\frac{2p}{(1-ε^2)} where F1 and F2 are two fixed points, and PF1 is the distance from P to F1 (similarly, P F2). F1 and F2 are...

I drew an oval using the ellipse tool of a vector-based drawing program. It's 23.5 mm wide and 21.5 mm high. There is a chord 15 mm long perpendicular to the minor axis. So the question is, how do I calculate the distance from the chord to the end of the ellipse (i.e., the end of the major...

Hey guys First real thread besides my introductory thread. I'm a Danish student in what is somewhat equivalent to my junior/senior year in the american school system. That was a small attempt at school system conversion. I'm writing a project about the black hole Sgr. A* in the centre of our...

Homework Statement Given the ellipse ##0.084x^2 − 0.079xy + 0.107y^2 = 1 ## Find the semi-major and semi-minor axes of this ellipse, and a unit vector in the direction of each axis. I have calculated the semi-major and minor axes, I am just stuck on the final part. Homework Equations this...

Homework Statement Suppose a circle of radius 'b' is set in motion.Calculate the relativistic speed parameter β(=v/c) such that the circle is seen as an ellipse of semiminor axis 'a' and semimajor axis 'b' where a <b.3 marks. Homework Equations L=L0/γ The Attempt at a Solution...

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? I used wolfram alpha equation solver, I tried to insert the equation of a line into the one of a...

Hello everybody, I'm trying to know, in a keplerian orbit, how to calculate the area of a swaped area; since the Sun is at one of the focus, I wish to calculate given an angle measured from focus to the orbiting body, the area swaped. I don't know if I'm explaning this right...Hope so...

Homework Statement ##\mathscr{C}## is an ellipse ##\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1## and ##\vec{F}(x,y) = <xy^2, yx^2>## write ##\displaystyle \int_\mathscr{C} \vec{F} \cdot d\vec{s}## as a double integral using greens theorem and evaluate Homework Equations ##\displaystyle...

Find equation for center at (1,2) and vertex at (1,8) and Minor axis length of 4?

347) An ellipse slmetric with respect to the coordinate axes handle: through the fixed point (h, k). Find The equation of the ellipse's? area maximum answer k2/SUP] h 2 + h 2 y 2 = 2 h 2 k2 The equations here must be y = m(x-h)+k Parametrizing x= a cos(t) y = b(sen(t) D= (a...

348) given the length of the ellipse to a2 h2 + b2y2 = a2 b2 Find the length of the tangent shorter, that intercepts between? the coordinate axes answer L = a + b The equations a2 h2 + b2y2 = a2 b2 And the line y = mx + b as the objetive function

Homework Statement To calculate I, the moment of inertia of an ellipse of mass m. The radius are a and b, according to the drawing. Homework Equations I=mr^2 Ellipse: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \Rightarrow y=b\sqrt{1-\frac{x^2}{a^2}} Area of an ellipse: \piab The Attempt at a...