Parametric equations Definition and 199 Threads

Homework Statement I've uploaded a scan of the questions. Questions 4, 5, and 6 are given in the 3 files uploaded. They all come from the given information from the first scan of the problem. Homework Equations The Attempt at a Solution I've worked everything I could on paper...

Homework Statement Find the area of the region enclosed by the parametric equation x=t^3-8t y=2t^2 The Attempt at a Solution I am not even sure how to start this problem. I read somewhere that to start with you solve for t in one of the equations. when i solve for t I end up...

Homework Statement i. x = 3cost, ii. y = 9sin2t, iii. 0\leq t < 2\pi iv.\int_0^\frac{\pi}{2} Asin2tsint \ dt 2. The attempt at a solution So this is what I am given and I am supposed to be able to show that this is the integral for the shadded area between the curve and the...

x = 2cot t y = (sin t)^2 t is greater than 0 but less than or equal to pi/2 The cartesian can be found using trig identities to be: y = 8/ (4+ x^2) What would be the range of the cartesian equation? I think it would be x is greater than or equal to 0, since when t = pi/2, x =...

Homework Statement A particle is located at r=(2i+4j)m at t=0s. At t=3s it is at r=(8i-2j)m and has velocity v=(5i-5j)m/s a)what is the particles acceleration vector a? Homework Equations r1=r0+v0(t1-t0)+1/2a(t1-t0)^2 v1=v0+at The Attempt at a Solution v1=v0+at...

I just have a question, when I am rotating something let's say around y=2 and the two equations are x=t^3 + 1 and y = 4t+1 how would i set it up?

Calculate the distance between the 2 lines and use this distance to prove that the are not going to intersect. x(t) = 2 + t y(t) = -1 –t z(t) = t x(t) = 3 – s y(t) = 1 z(t) = 1 + s I have no idea where to start with this question! please help!

Homework Statement x(t)=2t-1 y(t)=t^2 algebraically eliminate the parameter to create a rectangular equation Homework Equations There was an example in our book that showed how to do this if the two equations contained sine and cosine, however nothing was said if they didn't. I...

Homework Statement Find and verify parametric equations for an ellipse. Homework Equations x=acost y=bsint The Attempt at a Solution lets say the equation is x=3cost, y=3sint, domain: 0 to 2pi x2 y2 -- + -- = 1 a2 b2 point does verify when t=0 x=3, y=0 which =1...

Homework Statement Consider the curve of intersection of the cylinders [x^2+y^2=4] and [z+x^2=4]. Find parametric equations for this curve and use them to write a position vector. Homework Equations Thats what I am looking for. What to set t equal to. The Attempt at a Solution I set...

Homework Statement Show that every point on the line v = (1,-1,2) + t(2,3,1) satisfies the equation 5x - 3y - z - 6 = 0 Homework Equations The Attempt at a Solution So what I did was solve the equation v by adding the x,z,and z components to get x = 1 + 2t y = -1 + 3t z =...

My book really doesn't go into a lot of depth but I was wondering if this is correct If we are asked to find the tangent line of a specific value of t for a given parametric equation then we can find the equation of the tangent line in either rectangular or parametric functions. Rectangular...

Hey I have a problem with question 4 of this problem set http://www.physics.ubc.ca/~mattison/Courses/Phys170/p170-ps5.pdf Number 4. I have found Vmin to be 0.84m/s which i know it is correct, but i cannot solve Vmax? i thoguht you could maybe approach this question with 2 parametric...

Homework Statement At what point does the curve x = (1-2cos^2(t), y=(tan(t))(1-2cos^2(t)) cross itself? Find equations of both tangents at that point. Homework Equations The Attempt at a Solution To begin, I figured that x=y when it crosses itself, so I set x=y and got 1 = tan(t), so t=\pi/4...

i have a couple questions that confuse me that would help me on doing my homework on parametric equations... do the parametric equations x=t^2 and y=t^2 describe the line y=x? and if y is a function of t and x is a function of t, then is y a funcion of x? and last, does x=cos t, y=cos^2(t)...

I have an upcoming exam, and I'm having trouble grasping some concepts. The things that are currently perplexing me are parametric equations and rectangular equations and converting between the two. I have a problem like this Given the parametric equations x = e^(-t) + 1 and y = e^(-2t) -...

I am confused myself, so I post the Q. when we talk about "definite integral of area" in rectangular or polar coordinates, the "area" is quite clear, at least people do it in this way in general: rectangular coordinate: area between locus y=f(x) and x axis. polar coordinate: sector area...

I need samples of parametric equations: x=Fx(t); y=Fy(t); the samples must be useful or famous in math, physics or engineer, not be created randomly meaningless. one that I know is to describle ellipse: x=A*cos(t); y=B*sin(t); I need 2 or more good samples for my report. thanks...

What are you trying to do when you find parametric equations for a geodesic lines on a surface? Take the metric ds^2 = dq^2 + (sinh(q)*dp)^2 Are you simply trying to get q as a function of s? and p as a function of s? If so, why? Thanks

Determine the vector and parametric equations of the plane that contains point C(1,-2,6) and the z-axis I take this to mean that any point on the z-axis is valid so does that mean either (0, 0, 1) or (1, -2, 5) are also on the plane?

3-dimensional parametric equations [Updated] Look lower for update... Homework Statement Well, my problem is that I need to give some examples on 3-dimensional parametric equations. So far I've found out what parametric equations are, and more specifically what 3-dimensional parametric...

Homework Statement 5. Find parametric equations for the tangent line to the curve of intersection of the surfaces z^2 = x^2 + y^2 and x^2 + 2y^2 + z^2 = 66 at the point (3, 4, 5). The Attempt at a Solution f(x,y,z) = x^2 + y^2 - z^2 g(x,y,z) = x^2 + 2y^2 + z^2 Partial derivz...

I am trying to represent a helical pipe in x,y,z co-ordinants, would the x and y co-ordinants simply be multiplied by the equation of a circle if the growth of the helix is in the z direction? Any help would be appreciated. Thanks

Homework Statement Notice the curve given by: f(t) = x = 36-t^2 g(t) = y = (t^3)-25*t The curve makes a loop which lies along the x-axis. What is the total area insde the loop. Homework Equations Integral from alpha to beta of g(t)*f'(t) dt The Attempt at a Solution Ok, so I...

Hi, Can someone explain to me what a parametric equation is exactly? Why it is used (instead of a normal function)? In other words, what is the significance of it? Second, to be more specific, in my book, there is an example where r(t) 2 costi + 2sintj + tk t>0. Then what they say is...

1 If x = t^{3} - 12t , y = t^{2} - 1 find \frac{dy}{dx} and \frac{d^{2}y}{dx^{2}} . For what values of t is the curve concave upward. So \frac{dy}{dx} = \frac{2t}{3t^{2}-12} and \frac{d^{2}y}{dx^{2}} = \frac{2}{3t^{2}-12} So 3t^{2}-12 > 0 and t > 2 for the curve to be concave...

given x^2-y^2=1 find the parametric equation... i have no clue where to start... it looks like a cirlce equation but i know that not right so what the hell?

I find parametric equations to be simply amazing. I was wondering if there is a website, or better yet a book that covers them in more detail? I found it incredible how we can describe circles, ellipses, lines and other analytical geometrical shapes by them...so I wanted to know how deep...

considering the surface 25x^2+25y^2+4z^2=54 The parametric equation for a line going thought point P=(1,1,1) is x=1+50t y=1+50t z=1+8t A plane an equation for the tangent plane through P. Here's what I know: the equation for a plane needs a perpendicular vector to the plane and a...

Could someone please give me a clue how to solve these parametric equations or a starting position. torus specified by these equations x=(R+rcosΦ)cosθ y=(R+rcosΦ)sinθ z=rsinΦ calculate the normal to the torus N(θ,Φ) and entire surface area p.s anyone recommend a book or a...

If someone could check my work and make sure I'm doing these problems right, I would really appreciate it. 1.Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: x= h + r cos \theta , y= k + r sin \theta (x-h/r)^2 + (y-k/r)^2 = 1 2.Find the arc length...

Hello everyone, I'm having troubles seeing how this works. The directions are: Find parametric equations for the tagent line to the curve with the given parametric equations at the specified point. Here is my work and problem...

need parametric equations to the tangent line at the point (cos 0pi/6, sin 0pi/6, 0pi/6) on the curve x = cost, y = sint, z = t x(t) = ? y(t)=? z(t)=? now from my understanding, i have to find the derivatives of x, y, and z right? and i did this... now alll i should do is plug in the...

I was wondering what the surface area would be when the curve: x=e^tsint, and y=e^tcost where (t) is greater than or equal to (0) and (t) is less or equal to pi divided by (2). when it is revolved about a) the x-axis b) the y-axis (approximation...

(1)If you are given the parametric equations x = sin(2\pi\t) y = cos(2\pi\t) and 0\leq t\leq 1 how would you find the cartesian equation for a curve that contains the parametrized curve? Using the identity \sin^{2}\theta + cos^{2}\theta = 1 would it be x^{2} + y^{2} = 1 ? Thanks

Find parametric equations for the tangent line at the point (cos(-4pi/6),sin(-4pi/6),-4pi/6) on the curve x=cost, y=sint,z=t x(t) = _________ y(t) = _________ z(t) = _________ r'(t) = <-sin(t), cos(t), 1> r'(0) = <0,1,1> my answer: x = cos(-4pi/6) + 0t y = sin(-4pi/6) +1t z =...

I need to find a set of parametric equations for a hyperbolic paraboloid. The hint is that I should review some trigonometric identities that involve differences of squares that equal 1. The equation is: \frac{y^2}{2}- \frac{x^2}{4} - \frac{z^2}{9} = 1 And what I have is...

I've recently attempted the following problem, http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/June2001.html with the following solution http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/solutions/June2001.html I've managed to form the meaningful derivatives (as...

The following parametric equations trace out a loop x = 8 - 3/2t^2 y = -3/6t^3+3t+1 1.) Find the t values at which the curve intersects itself. wouldn't i just have to solve for t for one of the equaltion to find t? also, can you find the intersects using a TI-83 plus to check your...

find \frac{d^2y}{dx^2} as a function of t, for the given the parametric equations: x = 2-4*cos(t) y= 4+cos(t)^2 \frac{d^2y}{dx^2} = _______ dy/dt = -2*cos(t)*sin(t) second derv. 2*sin(t)^2-2*cos(t)^2 dx/dt = 4*sin(t) second derv. 4*cos(t) \frac{d^2y}{dx^2} =...

The circle (x-3)^2 + (y-4)^2 = 9 can be drawn with parametric equations. Assume the circle is traced clockwise as the parameter increases. if x = 3+3cos(t) then y= _______? wouldnt y just be 3+4sin(t)?

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...

Describe the motion of the particle with position (x,y) as t varies over the given interval. x=2+cost y=3+sint where t is greater than or equal to 0 and less than or equal to 2 pi i've tried to eliminate t and came up with y=3+sin(arccos(x-2)) i don't know if...

Our lecture today covered Equations of Lines and Planes in 3D. Is this the only approach to learning line and plane equations in 3-d? Honestly do we need r = ro + t*v? To me this seems like a very hard way to learn equations of lines and planes. Maybe I should learn it to be a...

??Parametric equations?? hey what's up, ok i have a question on differentiating parametric equations. The question says to find the equation of the two tangent lines to the curve. here's the equations... x = 6 cos t y= 2sin2t Now, after i differentiate them, do i just plug in...

Original question: a) Say r'(t) = 3t^2 i - cost j + 2t k, and r(0) = i + k. Find r(t). b) Find T(t). c) Find parametric equations for the tangent line to the curve at t=1. I have done parts a and b and got the following results: a) r(t) = t^3 + 1 i - sint j + t^2 + 1 k b)T(t) =...

How does one find the equation of a line from parametric equations? In spefiic I'm looking at this: x(t) = 1+2t , y(t) = -1 + 3t , z(t) = 4+t... I think i got to use something liek x-1/a = y-1/b=z-1/c or something like that. If what i just said is true, then I'm lost on what to do next...

I am asked to find the equation of the tanget line to the curve at the givien points. (y -y1 = m(x1-x)) The point is: (-2/sqrt(3), 3/2) Parametric Equations are: where t = theta x = 2*cot(t) y = 2*sin^2(t) How would i find what theta is in this set, inorder to solve dy/dx...

i have a geometry/algebra test tommorow and i have been sick for the whole unit, and my darn teacher is making me do it tommrow, even though i have no idea wuts going on...its on lines with parametric equations...if anyone has anything (tutorials, sites,etc.) anything that will help me...