Describe the relationship between the lines with the following parametric equations: x = 1- 41, y = 3+t, z = 8– 6t x = 2+ 3s, y = 2s, z =-1- 3s.

Q: Find three different pairs of parametric equations for the line segmentthat starts at (0, 0) and…

A: Direction ratio is = (6-0, 6-0)= (6,6) That is equivalent to (1,1) , (2,2) and (3,3)

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

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Q: Find two different parametric equations for the rectangular equation given. y=x* +3 (a) Substitute…

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Q: find parametric equations for the given curve.  4x − y 2 = 5

A: Given curve is 4x − y 2 = 5 To find the parametric equations :-

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: Find the parametric equation of the line ( x-3, y+6 )•( 2,-3 ) = 0

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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: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

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

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Q: Sketch the parametric curve of the given parametric equations and indicate the orientation. 1. x=3t…

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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: Consider the curve C given in parametric equations as

A: In this question, we find the tangent line and normal line along with that we find the point where…

Q: Sketch the plane curve represented by the parametric equations x = Vi and y = 2t – 1 by eliminating…

A: Sketch the plane curve represented by the parametric equations             x=t     and     y=2t-1 by…

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

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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: find the slope of the parametric curve x=-6t-5, y=3t^3, at the point t=3

A: To find the slope we have to find dy/dx For that we find dx/dt and dy/dt first

Q: Sketch the curve with parametric equationsx = 3t − 4, y = 3 + t^3

A: Here we have to sketch the curve with parametric equations.  x=3t-4; y=3+t3

Q: Find parametric equations for the given curve. (x - 1)2 + ( y + 2)2 = 9

A: Given: x-12+y+22=32 for any given curve equation x-a2+y-b2=r2, parametric equation of curve is given…

Q: Find parametric equations for the line through (-2, 0, 4) parallel to v = 2i + 4j - 2k

A: we know that parametric equation of line which passes through point x0,y0,z0 and parallel to vector…

Q: x = 12 + 3 y = 2t [-2, 2]

A: Substitute t value

Q: Match the given parametric equations with one of the parametric curves. x-3- sint, y = 5+ cost O A.

A: To sketch the given parametric equation :- x = 3 -sin t  and  y = 5+cos t

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

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Q: Graph the curve given by the parametric equations below, and show its orientation. x=2 sin t, y=2…

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Q: Eliminate the parameter of the pair of parametric equations. x = 3t, y = t + 7 O y = 3x + 7 O y = 3x…

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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: Find the parametric equations for the line through the point (5, 2, 9) and perpendicular to the…

A: The parametric equation of a line passing through the point and has a direction cosines <a , b…

Q: *) Write the parametric equations y = x = 4et, y = 8e-t as a function of x in Cartesian form. with x…

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Q: Find the length of the curve defined by the parametric equations

A: Given parametric equations are x=(5/6) t and y=5 ln((t/6)2-1) from t=7 to 9 W need to find length of…

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

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Q: Find the exact length of the curve described by the parametric equations. • x = 7+3t², y = 1 + 2t³,…

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Q: Complete the parametric equations of the line through the point (3,-7,-2) and perpendicular to the…

A: Given that, the equation of the plane is     -3x-y+z=2  and the point (3,-7,-2) The direction vector…

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

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Q: Write the parametric equations x=2sinθ,y=9cosθ,0≤θ≤πx=2sin⁡θ,y=9cos⁡θ,0≤θ≤π in the given…

A: Given information: The parametric equations are x=2sinθ            y=9cosθ             Can be…

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: 3t For the parametric equations: 39e2 and y = 16e %3D

A: We can find the answer as below.

Q: Find the slope of the line whose parametric equations are x=4t+6 and y=t-1

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Q: Complete the parametric equations of the line through the point (-3,1,-4) and perpendicular to the…

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Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

Q: Sketch the curve represented by the parametric equations x = e−t ,y = e2t − 1 (indicate the…

A: The given parametric equations of curves are: x = e^(-t) y = e^(2t) - 1 The graphs of these…

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

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + y…

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Q: Verify algabraically whether the parametric equation x(t) = 10-2.5t, y(t) = 1.5t and the rectangular…

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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: Select two different sets of parametric equations for the rectangular equation. X-9 3 Ox= t+ 9, 3 Ox…

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Q: Find two different sets of parametric equations for the rectangular equation  y = 4x + 1, t = −1 at…

A: Given equation is y=4x+1, t=-1 and the point is (-2,-7).

Q: Find parametric equations for the line through (8,4,6) parallel to the x-axis. X = y = - o <t< ∞

A: The equation passing through point (8,4,6). The parametric equation passing through point (8,4,6)…

Q: Sketch the curve represented by the parametric equations x = √t, y = t − 5 (indicate the orientation…

A: Given parametric equation, x=t         ...(1)y=t-5       ...(2)

Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = et –…

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