Find parametric equations for each of the following. The circle of radius 2, centered at (0, 3, 0) in the plane y = 3, oriented counterclockwise as viewed from the positive y-axis.

Q: Given the parametric equation: x=cos(3t), y=sin(3t), 0 less than or equal to t less than or equal to…

A: Given: x=cos3t ,y=sin3t, 0 ≤ t ≤ π2

Q: In the given equation as follows , sketch the curve represented by theparametric equations (indicate…

A: Given the parametric equations x = 1+1t, y = t -1 x = 1+1t ,      y +1 = t x = 1+1y+1xy+1 = y+2xy…

Q: -38, find parametric equations for the given curve. 3x 34. Segment joining (-3,0) and (0, 4)

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Q: 3 Find the distance of the point Q from the line L with the following parametric equations. x = -1+…

A: The given line is: x=-1+4ty=1+3tz=7-3t  To find the distance of the point Q 36-5 from the given line…

Q: Find the parametric equations for the ellipse y2 + 4x2 - 2y + 4x + 1 = 0. Hint: Use completing the…

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Q: In  the given question as follows , sketch the curve represented by theparametric equations…

A: Explanation: Given that: x=t+1y=t2 Concept used: 1.For rectangular equation rewrite the equation in…

Q: 2. Determine the ry-coordinates of the points where the following parametric equations will have…

A: Given : Parametric equations : x = 2sin t,  y = 4 cos t,  0 ≤ t ≤ 2π To find : xy coordinates…

Q: Find a rectangular equation of the portion of the cycloid given by the parametric equations x = a(θ…

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Q: 4. Convert the parametric equations into a single Cartesian equation and use this to sketch the…

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Q: 32. y=-4x+1 a. x=t b. . C. x =-4t /27

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Q: Which of the following correctly graphs the parametric equations x(t) V3t – 1 and - y(t) = -2t + 1?…

A: parabolas with a vertex(h,k)(other than the origin, we use the standard form(y−k)2=4p(x−h)(for…

Q: Sketch the curve represented by the parametric equations    x = et − 1,                    y = e3t…

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Q: Given the parametric equations, x = t - 1 and y = -t, find the point on the graph at time, t = 4.…

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Q: Determine the shape of each polar curve. 9r = 7 parabola 7 circle 9 r = 4 + 6 sin(0) ellipse…

A: Given :            r=7r=74+6sinθr=74+4sinθr=76+4sinθ

Q: The position of an object in circular motion is modeled by the given parametric equations. Describe…

A: We first eliminate the parameter t.  From x = 9 sin(t),  y = 9 cos(t) we get:

Q: Show by eliminating the parameter theta that the following parametric equations represent a…

A: Eliminate the parameter to form hyperbola

Q: Find the exact length of the curve described by the parametric equations. x = 5 + 3t2, y = 3 + 2t,…

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Q: A watermelon is launched by a catapult with an initial velocity of 89 feet per second and an angle…

A: x(t)=(89cos61∘)t, y(t)=−16t2 +(89sin61∘)t+9.    comparing with height equation; y(t)=−1/2(g)t2 +(v0…

Q: 4. Find the distance from the pole to the vertices, and then find the equation of the ellipse in…

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Q: Consider the following parametric equations x=3+2t -t y=t+1 , -1<t<3 Sketch the graph of the…

A: Given query is to find the graph of the parametric equation.

Q: Eliminate the parameter in the parametric equations a(t) = –8t – 9 and y(t) = –32t + 9 to write a…

A: Given parametric equations, x(t)=-8t-9 y(t)=-32t+9

Q: A bumblebee is flying so that its position is given by~r(t) = cos(2t), cos(3t),sin(5t) for the…

A: Before we start the problem let us get to know the formula first.

Q: The asymptotes of the graph of the two given parametric equations are 1 and y = x = t+1

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Q: Match the parametric equations with the correct graph. e0.9t t 0 cos(9t), y sin(9t), z e = ZA Z A 2…

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Q: Which of the following correctly graphs the parametric equations x(t) = v4t – 4 and - y(t) = 3t – 3:

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Q: A lizard moves through the plane with its position at t seconds given by the parametric equations…

A: parametric equations x=3cos(2pi t)+2, y= -6cos(2pi t)+1.

Q: II. Solve each of the following problems. A. Eliminate the parameter and sketch the graph of the…

A: We will sketch graph

Q: Find a parametric description for the unit circle, beginning at (0,1) at time t=0 , and completing…

A: Parametric equation

Q: Consider the parametric equations below. x = t2,    y = t5   Eliminate the parameter to find a…

A: We will solve for t from y = t5

Q: The following are the parametric equations for the motion of an object: x(t) = t cos (5t² + 2), y(t)…

A: Given a parametric equation, x(t)=t cos5t2+2,  y(t)=t2 ln(-5t)

Q: 6. Locate all the points (if any) of the horizontal and vertical tangents to the curve defined by…

A: Consider the given equations,x=t2-t,y=t3-3tFind derivative with respect to…

Q: Determine the xy-coordinates of the points where the following parametric equations will have…

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Q: Given the parametric equation: x=cos(3t), y=sin(3t), 0 less than or equal to t less than or equal to…

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Q: x = 1 + 4t,    y = 3 − t2

A: Here we extract t from the 1st equation then put this into second equation.

Q: Eliminate the parameter from the parametric equations: æ = 3 sin t y = 2+ cos t The resulting…

A: Given: x=3sint                                                                   ..1y=2+cost…

Q: Given the following set of parametric equations, find all points of horizontal and vertical…

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Q: 1. For the parametric equations x=-, 2t? ア= t>0 a) b) Eliminate the parameter to obtain an equation…

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Q: The parametric equations x = sect and y = tan t , 0 <ts 2n, represent hyperbola.

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Q: If the parametric curve starts at (- 2, – 9) when t = 0 and ends at (5, 7) att = 1, then find a, b,…

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Q: If the parametric curve starts at (5, 10) when t = 0 and ends at (3, 8) at t = 1, then find a, b, c,…

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Q: If a projectile is fired with an initial 37. Path of a Projectile speed of t, ft/s at an angle a…

A: To find the path of the projectile motion, write t in terms of x and obtain t=xv0cosα.…

Q: Given the following parametric equation of a torus if we have 0<g<x and 0<f<2x The cross-section of…

A: Option a

Q: find the parametric equation for each of the following a.) for the line of slope 2 passing through…

A: a) Firstly, we will find the equation of line of slope 2 passing through the point (-2,4) by using…

Q: 1. Sketch the graph of the curve represented by the parametric equations x = 4cost, y = 4sint 0sts…

A: We have to sketch the graph of the curve and find all points where the curve has a slope of 12.

Q: Find parametric equations for the segment joining the given points. (1, 3) and (3, 6) 0 sts1 c(t)…

A: Let p and q be the points (1,3) and (3,6) The parametric equation of the segment joining p and q is…

Q: question 1

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Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Circle:  x = h +…

A: x=h+r cosθ , y=k + sinθ

Q: 15) Find a set of parametric equations to represent the graph of y = 4x – 3 using the parameter t =…

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Q: (b) Find the graph of the parametric equations: I = sin 0, y = 3 – 2 cos 20

A: Plugging values of θ, to find the corresponding values of x and y: When…