Let L be the line with parametric equations

Q: Give a cartesian equation for the curve given by the parametric equations: 4t² - 4t, y = 14t².…

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Q: 7. A line has equation /:*-=-= 1:*=1==32₁2=3 x-1 y-2 -,Z=3 z a) Write the parametric equation for…

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Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

Q: - = + t, y = t? + 5, -2 sts 2 y y 10 -10 -5 -5 5 10

A: In this question, the concept of the parametric equation is applied. Parametric Equation  A set of…

Q: For the lines: L1: x=2-4t, y= 5t, z=1+2t L2: x=-7-k, y=2+3k, z= 5+k Find the parametric equations of…

A: The line passing through the point (a,b,c) and parallel to z axis is  (a,b,c)+t(0,0,1)  That is ,…

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

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Q: Q2/ Find the Parametric aned standand equatior of the line Hhat passer through Points (-2,1,0)…

A: The equation of line passing through given two points is given as follows:

Q: Give a parametric representation for the straight line segment from the point (1,-1,2) to the point…

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Q: Find a set of parametric equations of a line passing through the point (3,2,-1), parallel to the xz-…

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Q: Consider two non-parallel lines L1 and L2 in R2 with the following parametric equations: (3,6) +…

A: Given : L1 = (3, 6) + s(3, -4) and                   L2 = (-4, -6) + t(2, -4)

Q: Let / denote the line in R with equation y = = 3x - 2. Let Q = (2, -1). (a) Write the line / in…

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Q: Consider the line in R? given by the parametric equation (a, y) = (2, -3) + t(-2, -9) What is the…

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Q: Give the parametric curve: x = t3-6t2 y = t2-4t Does every horizontal line intersect the curve? Does…

A: Given: the parametric curve:

Q: Sketch the curve (x2 + y2 )3 =4x2y2 by converting to polar coordinate system

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Q: Find the parametric equations for the path of a particle that travels three quarters of the way…

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Q: What are the parametric equations for the line segment from (3,2) to (-10,5)?

A: To determine the parametric equation of a line segment.

Q: Describe the plane x = 4.

A: Given, plane x=4we have to describe the plane x=4

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…