find parametric equations for the given curve. . (x + 9) 2 + (y − 4) 2 = 49

Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y =f…

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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: The parametric equations for a line L₁ are as follows: x = −2+3t y = −4+6t z=-5-9t Let L2 be the…

A: The parametric equations for a line through the point (x0,y0,z0) and parallel to the direction…

Q: The parametric equations for a line L₁ are as follows: x=-4+6t y=3-4t z = 1+4t Let L₂ be the line…

A: The given problem is to find the point P on the line L2. Given Line L2 is parallel to line L1 and…

Q: find the parametric equation (linear). remove the parameter to find the equation. graph them.  c.…

A: The solution of given equations is given as follows . The graph is the straight line as given below…

Q: Graph the curve whose parametric equations are given and show its orientation. Find the rectangular…

A: Given x=8cost and y= 9sint where 0≤t≤2π   t x y 0 8 0 π/2 0 9 π -8 0 3π/2 0 -9 2π 8 0

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: To find a parametric equation of the line tangent to the curve of intersection of the surfaces at…

Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: The given parametric equation is: x=3+t and y=t2-5t, 0≤t≤6 Find the value of t, where y=0:…

Q: Let A = (1, -2, 2), B = (0, -1, 3), and C = (2,c4, c), where c is a real-valued constant. Find all…

A: Let A=(1, -2, 2), B=(0, -1, 3), and C=(2, c-4, c) where c is a real valued constant.

Q: Two objects E and F are traveling by the following parametrically defined functions x = 2t - 4…

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A: The given parametric equations  and .We have find the rectangular equation and sketch its graph with…

Q: 3t 1+f3.y te Consider the parametric equations x = 3t² ‡ 1+ 3,¹ -1. Its graph looks like this: = (a)…

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Q: Construct parametric equations describing the graph of the line passing through the following…

A: Topic = Coordinate geometry

Q: Find parametric equations for the line through the points P(-1,- 1, -4) and Q(-4,-7,7). O A. x-t-3 y…

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Q: The parametric equations for a line L₁ are as follows: x=-5-6t y = 1+6t Z=-2-4t Let L2 be the line…

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Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

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Q: The S.S. Minnow leaves port (whose coordinates are (0, 0)) and heads out to sea for a three hour…

A: The graph containing the position of the light house and the movement of the ship is shown below.…

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: