Parametric equations Definition and 208 Threads

Homework Statement Question is "The Cartesian equation of the plane containing the line x=3t , y =1+t , z=2-t and passing through the point (-1,2,1) is?" Homework Equations \begin{array}{l} n \bullet (r - r_0 ) = 0 \\ < n_1 ,n_2 ,n_3 > \bullet < x - x_0 ,y - y_0 ,z - z_0 >...

Homework Statement Consider the parameterization of the unit circle given by x=cos(3t^{2}-t), y=sin(3t^{2}-t) for t in (-\infty,\infty). In which intervals of t is the parameterization tracing the circle out in a clockwise direction? In which intervals of t is the parameterization tracing...

Homework Statement If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the accompanying figure, the circle in question is the circle (x^2)+(y^2)=1 and the tracing point starts at (1,0). The unwound...

Homework Statement Determine if any of the lines are parallel or identical L1 (x-8)/4 = (y+5)/-2 = (z+9)/3 L2 (x+7)/2 = (y-4)/1 = (z+6)/5 L3 (x+4)/-8 = (y-1)/4 = (z+18)/-6 L4 (x-2)/-2 = (y+3)/1 = (z-4)/1.5 Homework Equations L1 pt(8,-5,-9) V<4,-2,3> L2 pt(-7,4,-6) V<2,1,5> L3 pt(-4,1,-18)...

Homework Statement Let R be the region in the 1st quadrant in the region enclosed by x=2cos(\theta) and y=sin(2\theta) Suppose R is rotated around the x-axis. Find the volume of the resulting solid. Homework Equations The formula for the solid of revolution is: V= \pi\int...

Homework Statement Find a vector equation and parametric equations in t for the line through the point and parallel to the given line. (0, 12, -11) x = -5 + 3t, y = 4 - 2t, z = 1 + 8t Homework Equations x = x0 + at y = y0 + bt z = z0 + ct The Attempt at...

Here is my question: When given three distict points A, B, C, find the parametric equations for the plane throught these three points. I was able to get the plane through these three points, first of all by getting the normal vector n = ABxAC, then by multiplying this vector by...

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...

Homework Statement Find parametric equations of the osculating circle to the helix r(t)=cos(t)i+sint(t)j+tk corresponding to t=pi. Recall that the osculating circle is the best possible circle approximating a curve C at a given point P. It lies in the osculating plane (i.e., the plane...

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?

Let L be the circle in the x-y plane with center the origin and radius 57. Let S be a moveable circle with radius 30 . S is rolled along the inside of L without slipping while L remains fixed. A point P is marked on S before S is rolled and the path of P is studied. The initial position of P...

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)?