Ellipse Definition and 399 Threads

i added a file with the curve the is being asked to find an ellipse is given. its formula is x^2 + 2*y^2=8 . find the formula of the curve that is being created by the the centers of the perpendicular lines to the X axes and the ellipse. i tried to solve this question by...

I've been trying to understand exactly how the Lie derivative parallel transports a vector, by working out an explicit example: Lie dragging \partial/\partial x at (a,0) on the x-y plane anticlockwise along the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 I choose to parametrize the ellipse using...

How can one find the eq. of an ellipse given that the foci are (-2,0) and (2,0) and that the directrices are x=-8 and x=8?

How can one find the eq. of an ellipse given that the foci are (-2,0) and (2,0) and that the directrices are x=-8 and x=8?

I'm going to sketch the graph of the eq. 4x^2 + 9y^2 = 144 This is an ellipse with its center at the origo and major semiaxis 6 and minor semiaxis 4. But how do I find the foci?

Homework Statement Prove the reflective property of the ellipse. Homework Equations x^2/a^2 + y^2/b^2 = 1 (equation of ellipse) tan theta = m2-m1/(1+m1m2) m = (y1-y0)/(x1-x0) The Attempt at a Solution I apologize if this is to simple for this forum, not sure where else to put it...

This one question has me totally beaten. And I thought I was pretty good in co-ordinate geometry. Here it is: If the equation ax^2 + 2hxy + by^2 =1 represents an ellipse, find the square of the eccentricity of the ellipse. I know that the ratio of the distance from the directrix to the...

Homework Statement The problem is Find the equation of the line with a positive slope that is tangent to the ellipse (x^2)/9 + (y^2)/4 = 1 At x=2Homework Equations Now I know that to find the tangent, I find the derivative of the equation. So I got 2x/9 + 2y/4 dy/dx = 0But its this part...

I’m having trouble graphing this equation: 16x^2+9y^2=144 I have entered it into both my Algebrator program and the quickmath.com website. They both gave the same graph of the ellipse. In each case the major axis was vertical. With the Algebrator program it simplifies the above equation...

Is it possible to transform an ellipse x^2/a^2 + y^2/b^2 = 1 ("a" minor or major semiaxis) Into a rectangle? If so, how can I do it? I am not very familiar so please explain all the details. I know the transformation from a circle to an airfoil, but not this one.

ellipse - urgent help needed Hi there.. i have an exam tomorrow morning and can't figure this out. ellipse defined by 3x^2 + 2y^2 = k length of major axis is 6 find k? ok.. i know that the major axis = 2a, so in this case a = 3 the general form of an ellipse is x^2/a^2 + y^2/b^2 = 1...

An ellipse has an equation which can be written parametrically as: x = a cos(t) y = b sin(t) It can be proved that the circumference of this ellipse is given by the integral: \int^{2\pi}_0 \sqrt{a^2 \sin^2 t + b^2 \cos^2 t} \ \ dt Prove that, if a=r(1+c) and b=r(1-c), where c is a...

In Morris Kline's 'Calculus', he puts the ellipse equation in this form, b^2X^2+a^2y^2=a^2b^2, and says this is the best way to differentiate it; i did it thinking implicit differentiation and the product rule, but I'd get four terms on one side and two terms on the other side. He doesn't show...

Does anyone know an equation for an ellipse (or other conics) in intrinsic coordinates, that is direction and curve length. It's the sort of thing that looks like it should be simple, but I've a feeling it may in fact be somewhat messy.

Having trouble with this problem. "The mean distance from the sun to Mars is 141.7 million miles. If the eccentricity of the orbit of Mars is .093, determine the maximum distance that Mars orbits from the sun." So basically what it is asking for is half the length of the major axis right...

expressing points on an ellipse given the (x,y) of the foci and the sum of the radii Given the (x,y) of the 2 foci of an ellipse, and the sum of the radii from the foci, Is there an equation that will find the (x,y) of a point on the ellipse at a specified angle? Is there an equation to...

hi, i am secondary student, can anybody help me to find a site in proving ellipse shape of Earth orbit? and also those site which help you in understanding Principia?

OK I have a v-t graph and I wish to find the change in displacement/distance/position w/e. REFER TO THE PICTURE FOR THE ACTUAL QUESTION THANKS! (see the pic attached) My teacher taught me a method of seperating the LINE (ref.picture) into segments then calculating the area of each one then...

Is it possible to work out the centre of an ellipse? The question asks for the eccentric angle of the ellipse with the equation x²+9y²=13 at point (2,1)... I have no idea how to get this, I know that the angle would be arctan(1/2) if the ellipse was centred at (0,0) Thanks

How would I find the eccentricity of the ellipse: x^2/49 + y^2/64 = 1 :confused:

I was hoping you could give me a hint on how to find the equations of the axis of the ellipse of equation 5x^2-6xy+5y^2-4x-4y-4=0. I think this is supposed to be an exercise about lagrange multipliers or something related to the gradient, but i really don't know. I am clueless, i don't know any...

Let P(x,a) and Q(-x,a) be two points on the upper half of the ellipse \frac{x^2}{100}+\frac{(y-5)^2}{25}=1 centered at (0,5). A triangle RST is formed by using the tangent lines to the ellipse at Q and P. Show that the area of the triangle is A(x)=-f'(x)[x-\frac{f(x)}{f'(x)}]^2...

I'm asked to show that the total length of the ellipse x = a sin x y = b cos x, a>b>0 is L = 4a \int_{1}^{pi/2} \sqrt{1-e^2sin^2x} dx where e is the eccentricity of the ellipse (e = c/a, where c = \sqrt{a^2-b^2} I've tried a whole bunch of algebraic and trignometric manipulation...

An ellipse is defined by the equation \frac {x^2}{144} + \frac {y^2}{36} = 1. Determine the equation of the ellipse formed when the original ellipse has undergone a horizontal compression by a factor of 1/2 and a vertical expansion by a factor of 3. I'm not quite sure how to work out the...

This is a conic application question worth 8 marks You don't want your dog to run away so you place 2 steaks in the groud 4 metres apart and attach the end of a 8 metre long rope to each side of the stakes then you attach the dogs collar to a ring which slides along the rope. Describe the...

I'm assuming that given point can only have one tangent line because it's just the instantaneous slope at a point. If so, then how can an ellipse have two tangent lines at a point? Do they mean something else?

How would i do this question? A canal with cross-section a semi-ellipse of width 20 m is 5 m deep at the centre. Find the equation for the ellipse, and use it to find the depth 2 m from the edge. I think i have a way to get it using major axis length 20 and minor axis length 10, but what...

Describe a circle as an ellipse?? An ellipse is a stretched circle. Can you describe a circle as an ellipse? If so, what are the foci of the circle? What are the lengths of the minor and major axis? Would this circle satisfy the locus definition of an ellipse? I really don't know how a...

16x^2+9y^2+192y-36y+468=0 Was the original conic i had to conver this into standard form and got \frac {(x+6)^2} {9} + \frac {(y-2)^2} {16} =1 Im not sure if this is a horizontal or vertical ellipse

Find the equation of ellipse given vertices and focus Check please Hi the question is find the equation of the following ellipse, given vertices at (8,3) and (-4,3) and one focus at (6,3) Well I drew a digram with the 3 points First I found the midpoint of the given vertices to get the...

When in standard form how do you know whether the ellipse is horizontal or vertical? and how do you know what a= and b= for the major and minor axis, and vertices? How do you get the coordinates of the foci?

The ellipse \frac{x^2}{3^2} + \frac{y^2}{4^2} = 1 can be drawn with parametric equations. Assume the curve is traced clockwise as the parameter increases. If x=3cos(t) then y = ___________________________ wouldnt i just sub x into the ellipse equation and solve for y? well i did...

The equation Ax^2 + By^2 + Cx = 1 represents an ellipse. If A > 0 and B > 0, what conditions must be satisfied if the ellipse has it's major axis on the y-axis? The answer is " C = 0 and A > B" When I first wrote this question I thought A > B should have been A < B. So how do I figure out...

Problem I: (The coeffiecients throw me off, I don't know what I'm supposed to do with them) 9x^2 + 16y^2 = 144 Determine: a) coodinates of the centre b) lengths of the major and minor axes Problem II: Sketch a graph of the ellipse 4x^2 + (y+1)^2 = 9 PS: For...

Hello... Here is a problem in coordinate geometry, in particular about the ellipse. A point moves such that the sum of the squares of its distances from two intersecting straight lines is constant. Prove that its locus is an ellipse and find the eccentricity in terms of the angle between...

1. Find an equation of an ellipse with vertices at points (-2, 5) and (-2, -3), containing point (0, 3). 2. A bridge is to be constructed across a river that is 200 feet wide. The arch of the bridge is to be semielliptical and must be constructed so that a ship less than 50 feet wide and 30...

In an ellipse, with center (0,0) can you assume the focal radii to be equal to 2a? where 2a is the length of the major axis? how about with center (h,k)? I'm pretty sure I read before that u cannot assume it to be 2a in an ellipse, only in hyperbola's. BUt my teacher tells me otherwise...

I understand that this is a bit cheeky but I've found a problem on one of my mechanics problem sheets that is giving me a headache. As much as I could just ignore it I'd rather try and gain some more understanding of the vague world of rotation and orbit Even at this early stage I'm...

Ack, such a simple question, but I haven't worked with conic sections in years. Can anyone suggest an elegant way to show that x=f*Sin(wt+\theta) y=g*Sin(wt+\phi) is an ellipse? I've tried using a rotation matrix on standard parametric ellipse equations and then solving for the angle of...

|F||D|=1 is the simplest form of the law of lever in equilibrium. If |F|=|x-y| and |D|=x+y then |x^2-y^2|=1 is an real hyperbola. In this case the interaction is repulsive. If |F|=x-iy and |D|=x+iy then x^2+y^2=1 is an real ellipse or imaginary hyperbola. In this case the interaction is...

Could anyone direct me to an analytically correct algebraic formula for the Perimeter of an Ellipse based on either the eccentricity or the Semi-Major and Semiminor Axes other than the Elliptic Integral ? If so, how accurate will it be for relatively high eccentricities such as 0.9-1.0 ? Thanks.

Hi everyone. I tried solving these questions but can't seems to get anywhere. I am not used to questions like these specially word problems. Sorry if this is the wrong section. Question 1: The receiver of the satellite dish is at the focus of the parabola dish. The focus is 80 cm from the...

Find the volume of an ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 after being rotated over the x-axis.

If the area enclosed by an ellipse 4x^2+y^2=1 and its cross section is perpendicular to the x-axis then its volume is? I don't have the slightest clue how to do this? Maybe solve for 2y^2=1-4x^2 set the integral equal to pi times the intergral of 1/4 to 1 of 1-4x^2?

"Radius" of an Ellipse a couple things I'm trying to fit together. First: a planet orbits a sun (positioned at one focus) at an certain speed. At any given time of year it will be at that same spot year after year... i have little clue how to make that work or solve for it. Second: i need...

is there a formula to find the circumference of an ellipse?

The quadrant of the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2} = 1. lying in the first quadrant, revolves about the line joining the extremities of the major and minor axis. Show that the volume of the solid generated is \frac{\pi a^2 b^2}{\sqrt{a^2+b^2}} (\frac{5}{3} - \frac{\pi}{2}). I tried...

An ellipse on the xy-plane has foci at (-41, 23) and (115, 42). The ellipse is tangent to the x-axis. What is the length of the major axis of the ellipse?

I have two integrals to give the circumference of an ellipse. I can't solve either. First, using rectangular coordinates, 1/2s=S{[1+(f'(x))^2]^(1/2)}dx taken from x=-a to x=a Since, y^2=b/a(a^2-x^2) 2y*y'=-2bx/a y'=-bx/(ay) [f'(x)]^2=(x^2)/(a^2-x^2) At this point, I'm already...