A curve C is defined by the parametric equations x=. =r², y=r -3t .

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

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Q: Find parametric equations for each of the following. The circle of radius 2, centered at (0, 3, 0)…

A: We should understand that y is going to be constant  and is going to be 3   Now since r = 2 [given]…

Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

A: Given :                y = 2 x - 5  ,  t = 0        at point (3,1)

Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

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Q: By eliminating parameter t, sketch the parametric curve for the given parametric equations. Then,…

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Q: Find the parametric equations for the line in which the planes -4x +y+3= = 5 and 2x+y+ = 3…

A: Given that:-4x+y+3z=5    .............(1)2x+y+z=3          ..............(2)

Q: In each part, find an equation of the sphere with center (5, –8, –2) and satisfying the given…

A: Given  Centre of sphere is =(5,-8,-2)

Q: Write three different sets of parametric equations for the curve $y=\sqrt{x}$

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Q: Find a parametric description of the line segment with endpoints P(-1,3) to Q(3,-2)

A: The line segments with endpoints P(-1,3) to Q(3,-2)

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: Sketch the curve represented by the parametric equations x = 8 cos θ,            y = 8 sin θ…

A: given: the parametric equations of the curve are: x=8cosθy=8sinθ

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: x = e-', y = e2t – 1

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Q: Cannot solve

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Q: Sketch the curve represented by the parametric equations x = tan2 θ,             y = sec2 θ…

A: Given that, x=tan2θ, y=sec2θ

Q: In each part, find an equation of the sphere with center (2, –3, –3) and satisfying the given…

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Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

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

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Q: In each part, find an equation of the sphere with center (1, – 7, –8) and satisfying the given…

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Q: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

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Q: d) Find the parametric equations for the line of intersection of the two planes.

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Q: The angle and the parametric equations for the intersect line between planes a + y = 1, and 2r+y-2z…

A: Given, x+y=1, 2x+y-2z=2 we know angle between two plane is…

Q: ) Find parametric equations for the line segment starting at P(-1,-3) and ending at Q(6,-16).

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Q: A curve represented by the parametric equations a = et and y = e 24, will be Select one: О нурerbola…

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

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Q: Find the parametricequations of the line passing Through (-2,0,3) parallel to ū = 2i +49-2R.

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Q: Find parametric equations, in terms of t, of the line passing through (2, 2, 12) and parallel to the…

A: Given: The line is passing through 2,2,12. Also, it is parallel to the line: x=5-9ty=2z=4+t The…

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

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Q: Find the parametric equations for the line through the point (0, 1, 2) that is perpendicular to the…

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Q: In each part, find an equation of the sphere with center (5, –8, –4) and satisfying the given…

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

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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: Find the parametric equations of the li segment that passes through the point

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

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Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

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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: Sketch the curve represented by the parametric equations Lindices Orientation of the curve), and…

A: Topic :- function

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

A: Given, the surfaces:               x+y2+2z=4,   x=1  Point: (1, 1, 1) Let         z = 1-2t

Q: Find parametric equations for the tangent line to the curve of intersection of the following two…

A: We have to find parametric equations for the tangent line to the curve of intersection of the given…

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

A: Any point on the Cartesian coordinate system is defined as x, y. Start from the origin, move m units…

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

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Q: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

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Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: <3, 1, 1> +…

Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

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

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