The curve above is defined by which of the following sets of parametric equations?

Q: Write Parametric Equations to Represent a Curve for the given curve for the given definitio:

A: In question number 32, we are asked to form only parametric equations, that means equation of x and…

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

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Q: Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the…

A: Take different values of t from the given interval and then plot the corresponding points and…

Q: Find the parametric equations for the tangent line to the curve

A: Here we have to find the parametric equations for the tangent line to the curve,  x=t3-1, y=t2+1,…

Q: Complete the parametric equations for the line where the planes – 4

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Q: Find two different sets of parametric equations for the rectangular equation   y = 4/(x − 1)

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Q: The graph of the curve given by the parametric equations X=sint and y=cos2t IS à Select one: O ircle…

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Q: This is the problem  If a and b are fixed  numbers, find parametric equations for the curve that…

A: It is required to define the point P in a, b  and θ.

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

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Q: [Question 5] Write down a complete geometric description of the parametric curve x=2cos0,y=2sine,0s…

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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 & y=4+3 e-2t To eliminate the parameter t & to sketch the graph of…

Q: If a and b are fixed numbers, find parametric equations for the curve that consists of all possible…

A: Solution:GivenIf  a and b are fixed numbersTo find:The parametric equations for the curve…

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

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Q: Cannot solve

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Q: A curve is defined by the parametric equations z (t) = e-* and y (t) = e*. What is in terms of t ? A…

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Q: Find a parametric equations representation for the curve (x + 3) 2 . (y – 2)² 1 4

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Q: Find two different sets of parametric equations for the rectangular equation   y = x3

A: y=x3 Let x=t, then y=t3 Let x=t+1, then y=t+13

Q: Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve…

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Q: Graph the curve whose parametric equations are given. x= 5 sin t, y = 5 cos t; Osts 2 OA. O B Oc.…

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Q: Find the parametric equations of the line perpendicular to l1 and l2 that contains the point (-1.…

A: We have to find equation of a line which is passes through the point (-1,-1,-1) and Perpendicular to…

Q: Eliminate the parameter for the following set of parametric equations, sketch thegraph of the…

A: In the question it is asked to eliminate the parametric variable and sketch the graph of equation…

Q: If you are given parametric equations of a curve, what is the formula for finding its arclength?…

A: To write the arc length formula for the given types of curves.

Q: sketch and identify curve defined  by parametric equations {x= 3t + 2 y= 2t + 3

A: To find- Sketch and identify curve defined  by parametric equations. x = 3t + 2y = 2t + 3

Q: Which set of parametric equations represents the curve shown in the figure?

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Q: Graph the curve whose parametric equations are given. x = 2 tan t, y = 5 sec t; 0 <t < 2n

A: To draw the parameterized Curve.  Given that , x=2tan(t) , y=5sec(t) ; 0≤t≤2π.

Q: Determine the length of the parametric curve given by the following parametric equations

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Q: Let C be the curve with parametric equations

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Q: Suppose you have the parametric equations x = 4cos(6) y= 6sin( 6 ) %3D Eliminate the parameter and…

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Q: Which of the following sets of parametric equations correctly represents the curve above

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Q: The curve above is defined by which of the following sets of parametric equations? Select the…

A: Find the equation of the graph.

Q: Explain how a pair of parametric equations generates a curve in the xy-plane.

A: Our Aim is to explain the fact that how a pair of parametric equationsgenerates a curve in the…

Q: The position of an object at time tis given by the parametric equations

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Q: Sketch the curve represented by the parametric equations x = 1 + 8t,                 y = 3 − 4t…

A: x=1+8t,  y=3-4t When t=0, x=1+80, y=3-40⇒x=1, y=3 When t=1, x=1+81, y=3-41⇒x=9, y=-1 Now the graph…

Q: The graph of the curve given by the parametric equations x= sint and y=cos2t IS a

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Q: find parametric equations for the given curve. Line through (3, 1) and (−5, 4)

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Q: Find two different sets of parametric equations for the rectangular equation  y = x2

A: y=x2 Let x=3t, then y=3t2=9t2 Now let x=4t, then  y=4t2=16t2

Q: What curve is represented by the given parametric equations, show it on the graph including t, x =…

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Q: This is the problem    If a and b are fixed numbers, find parametric equations for the curve that…

A: Let the coordinate of point P is (x,y). In the triangle OCD, sinθ=CDOCsinθ=yby=bsinθ Similarly,…

Q: Eliminate the parameter in x = -t^2+9t and y = t-4 and then identify the parametric curve and sketch…

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Q: Determine whether the statement " The graph of the parametric equations      x = t2 and y = t2 is…

A: Given: The graph of the parametric equations      x = t2 and y = t2 is the line y = x

Q: Eliminate the parameter to find the Cartesian equation for the given parametric curve. = vt +1, y =…

A: Cartesian equations is x^2 - y^2 = 2

Q: Find the parametric equations of the line that is tangent to circle

A: Question (1) - Equation of circle - x2+y2 = 25Differentiating on both sides with respect to x -…

Q: Graph the curve whose parametric equations are given. x = -sec t, y = tan t; -<t<

A: x=-sec(t) y=tan(t) -π2&lt;t&lt;π2

Q: Determine the parametric equations of the path of a particle that travels the circle:

A: Given,        (x-4)2+(y-3)2=49 Time interval is 0≤t≤2π

Q: Under what circumstances can a graph that represents a set of parametric equations have more than…

A: On considering the parametric equations x=f(t) ----(1) y=g(t)----(2) Where, x and y is a function…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: