Ellipse Definition and 399 Threads

Homework Statement Find a vector-valued function f that traces out the given curve in the indicated direction. (a) Counterclockwise (b) Clockwise. 4x2+9y2=36 Homework Equations x2+y2=r2 cos2t+sin2t=1 The Attempt at a Solution From what I can determine, this is an ellipse. I...

Hi Let's say that we have equation of circle as x2 + y2 = R2 and equation of ellipse in quadratic form as A x2 + B y2 + Cx + D = 0 if the circle is inside the ellipse, so there is no intersection ... Are x and y imag in this case? /or/ is one of them imag and the other is real...

Homework Statement intersection x^2+y^2+z^2=4 and plane y=z Homework Equations n/a The Attempt at a Solution so, i solve it simultaneously, and get the equation of ellipse x^2+2y^2=4. but what does the ellipse tell me? is that the points of the intersection?, but aren't it...

Hi..I have a basic question regarding the equation of an ellipse. Let's say I ahve an ellipse with major and minor axes 2a and 2b respectively. Now, to check whether a point lies inside this ellipse, its fairly simple...I can just use the standars ellipse equation for that. Now, if my major axis...

Homework Statement There is an elliptical path and pegs A and B are restricted to move around it. If the link moves with a constant speed of 10m/s, determine the magnitude of velocity when x=0.6m [PLAIN]http://users.adam.com.au/shortround/Prob.12-78.jpg Homework Equations...

The problem is formally attached in the PDF. I did not see it fit to post my problem on the forum itself (sorry). Any assistance is appreciated. Thanks.

Homework Statement Consider the ellipse given by the parametric equation x=3cos(t) y=sin(t) 0\leqt\leq2\Pi. Set up an integral that gives the circumference of the ellipse. Also find the area enclosed by the ellipse. Homework Equations \int\sqrt{1+(dy/dx)^2}dt The Attempt at a...

The standard method of calculating area of ellipse: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 Area = \int_C -ydx \hbox { or } \int_C xdy It is more convient to use polar coordinate x=a cos \theta \; \hbox { and }\; y=b sin \theta dy = b cos \theta \hbox{ Using } \int_C xdy =...

Homework Statement Find the points on the ellipse x2 + 2y2 = 1 where f(x,y) = xy has its extreme values. Homework Equations The Attempt at a Solution f(x,y,z) = x2 + y2 + z2 -- constraint g(x,y,z) = x2 + 2y2 -1 = 0 gradient of f = \lambda * gradient of g 2xi + 2yj + 2zk =...

Hi, If the cone is cut with a plane such that an ellipse has been formed. Let's say the major axis is 'a' and the minor axis is 'b'. Is there a way to find a and b from the geometry instead of getting them from the quadratic equation.

I hope this the right place to post my question... should it be, "we can define a as half the sum of distances..."? please correct and explain if I'm mistaken thanks

i'm having trouble creating a arc for check for collision similar to a grenade launcher type weapon and am not very good at math :/ i have the player position and the target position, now i just need to check every so often (let's say .1 units) along the outside of my ellipse to see if my...

Let us consider the Electric field components of a polarized EM wave . [PLAIN]http://www.cdeep.iitb.ac.in/nptel/Electrical%20&%20Comm%20Engg/Transmission%20Lines%20and%20EM%20Waves/graphics/CHAP%204__255.png. Now if we fix the value of z (for convenience take z=0) and consider the locus of...

Homework Statement Describe the shape of each level curve for the following function: z= (5x^2+y^2)^.5-2x Homework Equations I would like to prove that the curves are elliptical by setting z as a constnat and algebraically putting the equation in standard for for an ellipse...

Hello all, I am neither a physicist nor a mathematician, I am an archaeologist trying to develop a mathematical model for archaeological site detection. The problem is set up like this (and hopefully this will make some sense): The detector moves in parallel transects that can be of any...

Hi when we use standerd Equation of an ellipse here 2 formula 1 and 2 when we use 1 and when we use 2 hlep me

Homework Statement 6x2 + 8y2 + 32y - 16 = 0 Homework Equations The Attempt at a Solution I think I made a mistake. This is how far I got 4(x-4)^+3(y+9)^=120 I made a mistake. Can someone delete this thread? What did I do wrong?

Homework Statement Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed in the ellipse x^2 + 4y^2 = 4 Homework Equations The Attempt at a Solution I simplified the equation of the ellipse into the ellipse formula: x^2/4 + y^2 = 1...

Hi everybody, Guys I'm a total stranger to physics. I need some help to find the relationship between the major/minor axes of an ellipse and the radius of a sphere in a cone of light. For example, imagine a light source is located at 'h' height from a plane and a sphere(with a radius of...

Homework Statement Assume that the surface S which delimits the 2 mediums is a revolution surface around the z-axis. Light rays start at point F_1 and all the rays going through the surface reach the plane \Sigma in a same amount of time. Show that S is the result of rotating an ellipse with...

Calculus Question - Tangents to an ellipse - its got me stumped! Homework Statement A tangent line is drawn to the ellipse x^2/25 + y^2/16 = 1 so that the part intercepted by the co-ordinate axis is a minimum. Show that it has a length of 9 units. Homework Equations x^2/25 + y^2/16 =...

Homework Statement Graph the following: 15(x+2)^2 + \frac{(y+3)^2}{4} = 4 Homework Equations \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 The Attempt at a Solution I can't seem to get both coefficients to 1, since the right side is only 4. If I multiply the whole thing by 4, I can...

Hey what is the directrix when talking about an ellipse? I found a book that finally shed light on what eccentricity was, but there's still no mention of what the directrix is. To be honest, it doesn't even explain eccentricity but I intuitively understand it, however the directrix is...

Homework Statement A rectangle is placed symmetrically inside an ellipse (i.e. with all four corners touching the ellipse) which is defined by: x^{2} + 4y^{2} = 1 Find the length of the longest perimeter possible for such a rectangle. Homework Equations Within the problem...

This is a small part of a larger program I'm working on. This actually looked like a fun problem -- but I'm hitting a wall now. Imagine a person riding a bicycle. You know their starting position (X1, Y1), and their initial heading. Their destination is elsewhere at point (X2, Y2). They...

Volume by cross-section: ellipse and equilateral triangle cross sections?? Homework Statement The base of a solid is the region bounded by the ellipse 4x^2+9y^2=36. Find the volume of the solid given that cross sections perpendicular to the x-axis are: a) equilateral triangles b) squares...

Homework Statement What is \int_{\gamma} xy dx + x^2 dy in each of the following cases? 1. \gamma is the lower half of the curve 2x^2 + 3y^2 = 8, traveled from (2,0) to (-2,0). 2. \gamma is the full curve 2x^2 + 3y^2 = 8, traveled counterclockwise. Homework Equations The line...

Please tell me how to find the orbital energy of ellipse and hyperbolic trajectory. Thank you.

given an ellipse in vector form r(phi)=a*cos(phi)i +b*sin(phi)j where i and j are the unit vectors for x and y, then y= b*sin(phi), and x = a*cos(phi). tan(phi) = y / x , but y/x=(b/a)*tan(phi) which implies 1 = b/a or b=a which is false. What is the deal? doing the same for a...

I want to figure out the 'a' of an ellipse (i.e. (major axis)/2) by knowledge of it's circumference and length of minor axis. Using my little knowledge which I gained from reading (roughly) the ellipse article of wikipedia; I realized that I need to use that notorious and approximate...

Please Help! Line passing through an Ellipse and a Point Homework Statement Hi guys, I'm new to the forum and I could really use some help with this problem. There is an ellipse with the equation: (X^2/4) + Y^2 = 1 There is a point on the graph (4,0) Find an equation that passes through...

Homework Statement i want to derive a formula for an ellipse sector. ellipse is not rotated and its center is in the origin. its semimajor and semiminor axis are a and b, respectively, and angle of the sector begins with t1 and ends with t2. it's just a simple surface integral in polar...

Hi, I am having some 2d and 3d data files (from some nmr experiment, as a matter of fact) and the data plot for that is such that most of the points are coming together now I want to draw ellipse around 2d data point and ellipsoid around 3d data point with the condition that 90% (or any...

Homework Statement The area of the ellipse \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 is given by \frac{4b}{a}\int_{0}^{a}\sqrt{a^{2}-x^{2}}dx . Compute the integral. Homework Equations The Attempt at a Solution I know I have to let x=asin\theta and then dx=acos\theta . Then I plug in x. Do I...

Homework Statement Find the equations of both the tangent lines to the ellipse x2 + 9y2 = 81 that pass through the point (27, 3). One is horizontal the other is not. Homework Equations The Attempt at a Solution horizontal, easy: y = 3 x^2+9y^2=81 derivative: 2x +...

Homework Statement Find the tangential and normal unit vectors for an ellipse with major axis of length a in the x-direction and minor axis of length b in the y-direction. Homework Equations For a circle, the unit vectors are defined as \hat{r}=\cos{\theta}\hat{i}+\sin{\theta}\hat{j}...

Homework Statement The vertex of the parabola y^2=2px is the center of an ellipse. The focus of the parabola is an end of one of the principle axes of the ellipse, and the parabola and ellipse intersect at right angles. Find the equation of the ellipse. Homework Equations...

perimeter of an ellipse -- exact formula I found an exact formula for the perimeter of an ellipse in terms of its major and minor axis a = 1/2(major axis) b=1/2(minor axis) my equation for the perimeter of an ellipse...

Homework Statement Find the equation of the line perpendicular to the ellipse x^2 − xy + y^2 = 3 at the point (-1,1). Where does the perpendicular line intercept the ellipse a second time?Homework Equations ?The Attempt at a Solution I have already found the equation of the perpendicular line...

I have the solution to a problem and I need help understanding how the solution was obtained. I have to take an equation of an ellipse and transfer it to parametric form. The ellipse has the equation: (x+1)^2 + 4y^2 = 4. The solution has the ellipse parameterized as follows: x+1 =...

Homework Statement Prove that the area of an ellipse with equation \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 is A=\pi ab. Homework Equations The Attempt at a Solution I solved for y, set up the integral for area with lower limit -a and upper limit a, did u substitution...

Homework Statement Let \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 be the equation of an ellipse with vertices (\pma,0) and (0,\pmb), and a slope m= -0.5 in the point (1,1). Find a and b.The Attempt at a Solution So far I've solved for a and b in relation to each other, but I'm not sure how to...

Homework Statement Find the length of the ellipse 9x^2 + 10y^2 = 90 correct to six decimal places.Homework Equations 4Larc in the first quadrant = Lellipse The Attempt at a Solution Just checking to see if I did this right: 9x^2 + 10y^2 = 90 x^2/10 + y^2/9 = 1 Therefore a = \sqrt{10} and...

Hello everyone, I am still relatively new to this site, so any mistakes I take full blame for. My question is: At what point(s) on the ellipse x^2+4y^2=4 is the slope of the tangent line 1/2sqrt3? I have found the derivative of the equation through implicit differentation (I came out with...

If (5,12) and (24,7) are the focii of a conic passing through the origin, then find the eccentricity of the conic Attempt: Found the centre as (h,k), midpoint of the given points. (x-h)^2/a^2+(y-k)^2/b^2=1 i put x=0 and y=0 as it passes through the origin. from the equation e^2=1-(b^2/a^2)...

Homework Statement What is thea are of the largest rectangle that can be inscribed in the ellipse 4x^2 +9y^2 = 36 A) 6 rad 2 B) 12 C)24 D) 24 rad 2 E) 36 Homework Equations Must be done using optimization and first derivitive The Attempt at a Solution I know I have to use A=...

Homework Statement Prove that the straight line x cos @ + y sin @ = p is a tangent to the ellipse x2/a2 + y2/b2 if a2 cos2@ + b2 sin2@ =p2 . u and v are the perpendicular distances of a tangent from the two points M(0,ae) and N(0,-ae) respectively. Prove that u2 + v2 is a constant...

Find Curvature of Ellipse given x=3*cos(t) and y=4*sin(t) at the points (3,0) and (0,4) Relevant equations: curvature at r(s) is k(s)=||dT/ds|| when r(s) is arc length parametrization and T is the unit tangent vector I usually use the formula k(t)= (||r'(t) x r''(t)||)/||r'(t)||^3 So...

Homework Statement an ellipse has the vertices (+&-4, 0)and the point (1,2) lies on the ellipse. find the standard form of the equation of the ellipse . Homework Equations (x-h)^2/a^2 + (y-k)/ b^2 = 1 The Attempt at a Solution (x-0)^2/(4)^2 + (y-0)/b^2 = 1 (1-0)^2/16 +...

An ellipse is a conic section. If you construct an ellipse using a cone, does the axis of the cone cross through one of the foci of the ellipse? if so, how can this be shown mathematically? This is just purely out of curiosity.