1. (a) Sketch a curve represented by the parametric equations x = 1 - t² and y = 1+t. Then find a rectangular-coordinate equation for the curve by eliminating the parameter.

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

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Q: Find the distance between the point  and the line given by the set of parametric equations.…

A: Answer

Q: (a) Find the parametric equation of the line that contains the two points A = (-4,0, –1) and B (3,…

A: (a) Here first we find vector v = AB = OB-OA, then the equation of line will be (x, y, z) = A + t v…

Q: 3. Find a rectangular equation to represent the plane curve. x = 3 tant, y = 2 sect for tin (-7-7)

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Q: Consider the parametric the curve defined by the equations x = t² – 2t + 2 and y = t² + t. (a) The…

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Q: Write the Cartesian equation of the line given by the parametric equations æ(t) y(t) z(t) 5 – 4t -1-…

A: Givenx(t)=5-4ty(t)=-1-6tz(t)=6tIt means thatx-5-4=ty+1-6=tz-06=tcan also be written…

Q: 5. Graph and find the parametric equations for the line through the point (1, -2, 3) and parallel to…

A: This question is about application line in 3d

Q: ) (i) Find the parametric equations for a smooth curve, C: x= 4z, y = -3z that joins two points,…

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Q: Find a parametric equation for the line through the point (2,3, – 1) and perpendicular to the plane…

A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

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

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Q: 3. Consider the parametric equations x = 3 cos@ and y=2 sin 0, for 0≤0<2m. (a) Sketch the curve by…

A: Note : As per our Guidelines , we can solve first question. please repost remaining one.

Q: The parametric equations r = 3 - t, y = 2t + 4, 0 <t < 2 describes motion along a certain line…

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