2. Find the point(s) of intersection of the following two parametric curves, by first eliminating the parameter, then solving the system of equations. x =t+5, y=t² and x = 16 -t, y = t a. (25, 400) b. (1, 16) c. (400, 16) d. A and B e. A and C

Q: Which of the following correctly gives the Cartesian form of the parametric equations x(t) = –7t – 2…

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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: In the given equation as  follws , find a set of parametric equations forthe rectangular equation…

A: Given :                 y = 2x -5 , t=0 at point (3,1)

Q: Find the exact length of the curve described by the parametric equations. x = 5 + 6t², y = 3 + 4t³,…

A: Find the length of the curve   x= 5+t2 ,y= 3+4t2 , 0<=t<=1 .

Q: For the parametric equations: a = 12e2t and y = 23e3t %3D da (i) dt dy (ii) dt dy (iii) dx ||

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Q: If x(t)=9sint+2 and y(t)=5cost+5, eliminate the parameter to write the parametric equations as a…

A: sin2t + cos2t = 1

Q: oblem 20. Does the line with parametric equation x = 21 + 1, y = 3t- 2, z = 2t – 2, 1 e R intersect…

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Q: Given that x(t) = 10t + 2 and y(t) = –30t – 6, which of the following gives a Cartesian form of the…

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Q: A parametric curve is given by the equations: x (t) = 3 – t, y (t) = 2t, 0 <t < 3. After eliminating…

A: The given parametric curve is  x(t) = 3-t, y(t) =2t,   0≤t≤3 Here,  parameter is t.   We have to…

Q: Given the parametric equations, x = 3/t and y = t - 2, eliminate the parameter. y = --2 y = +2 y =…

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Q: Which of the following is not an equivalent rectangular equation for the following parametric…

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Q: Eliminate the parameter in the parametric equations x(t) = -6t + 8 and y(t) the equations. = 30t –…

A: givenx=-6t+8....................(i)and y=30t-10...................(ii)x=-6t+86t=8-xt=8-x6

Q: Eliminate the parameter to write the parametric equations as a Cartesian equation. If x(t) = 3t – 2,…

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Q: Convert the following lines to parametric equation. a) l₁: = (1,0,1) + t(1,0,−2), t = R Z-3 b) 1₂: x…

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Q: i) Eliminate the parameter for the given set of parametric equations, sketch the graph of the…

A: Given: x=6-7 e-2t &amp; y=4+3 e-2t To eliminate the parameter t &amp; to sketch the graph of…

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 particle moves on a trajectory described by the parametric equations x(t)=2t, y(t)=8t, t≥0. What…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: a +…

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Q: Graph the plane curve defined by the parametric equations:x = t2 + 1 ,  y = 3t ,  -2 ≤ t ≤ 2.

A: Consider the given parametric equations x=t2+1 and y=3t over the interval -2≤t≤2 now, make the table…

Q: For the parametric equations: a = 12e and y = 29e3t dr (i) dt dy (ii) dt dy (iii) dr || ||

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Q: Graph the plane curve defined by the parametric equations: x = t2 - 1, y = 2t, -2 ≤ t ≤ 2.

A: we have to graph the plane curve defined by the parametric equations: x=t2-1y=2t-2≤t≤2

Q: Q2:- Find the parametric equations for the following Cartesian equations. 1) x=(/y² + 4 + 2) 2) 4x2…

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Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t², y = 9+ 4t³,…

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Q: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

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Q: 18. What is the rectangular equation of the curve whose parametric equations are x = 2t, y= 2+ 3t*?…

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Q: Show that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line…

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Q: Question 2. (a) Prove that the lines with parametric equations: x = 1+t, y =1+ 6t, z = 2t and x = 1+…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Eliminate the parameter in the parametric equations #(t) = 2t + 5 and y(t) = 8t equations. Provide…

A: In this question we will simply eliminate parameter t and get an equation between x and y. Solution…

Q: please make the curve easy to read and determine the direction (clockwise or counterclockwise) of…

A: Data given  X=-t+3   Y=-2t+1  value of t is given in a interval of [0, 5] Find out orientation of…

Q: Find the rectangular equation for the following two parametric equations. x = 2t – 1 and y = t² + 6…

A: Given equation is  x = 2t-1            ..............(i) And y = t2+6          .............(ii) So,…

Q: Given the planes 3.x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (b) Find parametric…

A: I have solved using an intersection point and direction ratios

Q: The motion of a particle in space is defined by the parametric equation x(t)=-t2+3t+1,in meter and…

A: To find the position of the particle, use the formula, r→(t)=x(t),y(t), where x(t) is the…

Q: What is the length of the curve defined by the parametric equations æ (t) = t² – 2t and y (t) = t³ –…

A: If x=f(t) and y=g(t)are parametric equations of the curve where t ranges from t1 to t2then…

Q: Consider the parametric equations x = √t − 2 and y = (1/ 2)t + 1, t ≥ 2. What is implied about the…

A: Consider the given parametric equation as x=t-2 and y=12t+1

Q: Graph the plane curve defined by the parametric equations:x = t2 - 1 ,  y = 2t ,  -2 ≤ t ≤ 2.

A: The given curve is x = t2 - 1 ,    y = 2t ,    -2 ≤ t ≤ 2. Sketch the graph as shown below.

Q: Eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint. 2 x2 + y2 = 36 x2…

A: We have to eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint.

Q: Consider the following parametric curve. Answer parts a and b.  x=−3+3t​, y=4−9t​;t=2

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Q: Andy and Donald are both running toward the soccer ball during a game. Andy's path is represented by…

A: They will collide when their respective x coordinates are equal and their respective y coordinates…

Q: Which of the following is the parametric equation of the line through the point (1,2,3) and parallel…

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Q: For the parametric equations: a = 16et and y 18e %3D da (i) dt 32*e^(2t) %3D dy (ii) dt 54*e^(3t)…

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Q: What is the parametric equations of the line through (2,2,2) parallel to the x- axis ? a) x = 2, y =…

A: 7) The Parametric equations of the line through (2, 2, 2)  parallel to x-axis is given…

Q: Given the parametric equations I = dy 9t2 and y = 4t, then %3D 2t Windows bD

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Q: Find the (perpendicular) distance from the line given by the parametric equations ¤(t) -2 – 2t y(t)…

A: Solution: The objective is to find the perpendicular distance

Q: Eliminate the parameter t to find a Cartesian (rectangular) equation in the form x=f(y) for the…

A: Topic = Algebra

Q: Given the parametric curve: x = t3-6t2 y = t2-4t What are all the points that the curve passes…

A: Given: the parametric curve:

Q: Find parametric equations for the given curve. 9x2 + 4y2 = 36

A: Given -            Parametric equation -              We define x and y both in terms of a third…

Q: What is the Cartesian form of the parametric equations æ(t) = 4cost – 1 and y(t) = 5sint + 2?…

A: Here I am attaching image so that you understand each and every step.

Q: Find the length of the curve given by the parametric equations z = 2t3/2 0 <t< 4 ' y = 3t + 1

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