1. The path of a particle is described by the parametric equations: x = 3t? + 1, and y = 2t + 1, -2

Q: List all of the points (x, y) on the parametric curve t° + 4t, y = 6t? where the tangent line is…

A: Given that, Parametric equation of the curve are following, x = t3 + 4t,      y = 6t2 and the…

Q: In Exercises 23–38, find parametric equations for the given curve. 25. 4x - y2 = 5

A: For the given curve:                                     4x-y2=5   To determine:…

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

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Q: find a parametric equation for the line that is per-pendicular to the graph of the given equation at…

A: 41. Here the given as  Now we let

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

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Q: 12- Find an equation of the tangent plane to the given parametric surface at the specified point.…

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Q: Find the parametric equations of a vertical line through point (0,9). Assume v = 0 corresponds to…

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Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

Q: find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

A: Find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

Q: The parametric equation of the line resulted from intersection of x-y 0, and z = 2 is %3D

A: Use the given planes.

Q: Suppose a curve is given by the parametric equations x = f (t), y = g (t), where the range of f is…

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Q: Suppose parametric equations for the line segment between (-2, 8) and (7,3) have the form: a + bt…

A: This question can be solved by substituting the values of x,y and t in the given equations.

Q: The graph of the curve described by the parametric equations x = 2t2 and y =t³ – 3t has a point…

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Q: Suppose parametric equations for the line segment between (-2, 10) and (8, 9) have the form: a + bt…

A: Note: As per our company guidelines we are supposed to answer the first question. Kindly ask the…

Q: x = 2t2 – C : 3t + 1 y = et²-1

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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: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

Q: 2) Graph the x, y-curve described by the parametric equation by eliminating t from the equation. x =…

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Q: Suppose a parametric equations for the line segment between (5,2) and (7,8) have the form:  x(t)=…

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Q: Suppose a curve is traced by the parametric equations x= 6.08 sin(t) and y = 22 -…

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Q: Find the set of parametric equations of the line through the point (1, 6, 3) that is parallel to the…

A: The direction ratio of the line x=6+5t, y=6+2t, z=4+2t is (5,2,2). Parallel lines have the same…

Q: What is the rectangular equivalence to the parametric equations? z (8) = 4 cos 0 + 2, y (8) = 2 sin…

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Q: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

A: Parametric equations of a line passing through the point P(a,b,c) and parallel to the vector v→=…

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

A: Given that z=x2+y2 and 3x−5y+7z=24 and point is 3,4,5. Let fx,y,z=x2+y2−z and gx,y,z=3x−5y+7z−24 We…

Q: A particle moves in space along a path whose parametric equations are given by x1 = b sin(wt), x2 =…

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Q: Find the length of arc of the curve given by the parametric equations x = t°, y=t² from the point…

A: Arc length is given byL=∫abdxdt2+dydt2dt

Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

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Q: A particle is moving along the curve given by the parametric equations x=1+t, y=1−t. Determine the…

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Q: A particle moves in space along a path whose parametric equations are given by bsin(wt), x2 =…

A: Image is attached with detailed solution.

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

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

A: Substitute t value

Q: In an open space, Thomas throws a ball at an angle of 70° to the horizontal with an initial velocity…

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Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

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Q: Suppose parametric equations for the line segment between (0,-10) and (8,-1) have the form: a + bt…

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Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 3x + 4y +…

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Q: Find parametric equations for the path of a particle that moves along the curve y=x from (1, 1) to…

A: Given Parabola is y = x²

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

A: Let's find.

Q: 10. Find the value of 2 for the parametric curve xx= y = 2t2 -6 at the point (1.-6).

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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: Find the parametric equation of the line tangent to the curve of intersection of the cylinder…

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Q: I need to get the parametric equation for a line between the points (0,1,2) to (3,0,-1). I have the…

A: Line passing though the points 0, 1, 2 & 3, 0, -1. Now let, x0, y0, z0=0, 1, 2 & x1, y1,…

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 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 given curve. Segment joining (1, 1) and (2, 3)

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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: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…

Q: Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z…

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