Find parametric equations for the path of a particle that moves along the curve y=x from (1, 1) to (-1, 1), and back to (1, 1). Use 0sis1 as your parameter.

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

A: Consider the given parametric equations, xt=tyt=e-4tzt=5t-t5 Here we need to find the parametric…

Q: Find parametric equations for the tangent line of the curve r(t) = (3+ 3/7, to – 5t2 + 4, 3t³ + 2t²…

A: Find the parametric equations fot the tangent line

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

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Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

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Q: Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y²…

A: We know that tangent line to ellipse will be perpendicular to normal of both the surface. Therefore,…

Q: find parametric equations for the given curve. y = x2, translated so that the minimum occurs at…

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Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x - 5 between…

A: formula:

Q: Find two different sets of parametric equations for y = x2 + 6.

A: Our Aim is to find the two different sets of parametric equations for y=x2+6

Q: Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line…

A: Given that: Equation of line is:     x=-1+3t, y=2-2t, z=3+t  and the point is : P(-2, 0, 3)

Q: 2. Find the parametric equations of the tangent line to the curve as result of the intersection of…

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Q: Find the slope of the curve whose parametric equation is given by y = t³ + t²+ 1/t and x = t⁴ + 3t²…

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Q: Find parametric equations and a parameter interval for the motion of a particle starting at the…

A: Given,

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: 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 a-tcost, y-t, z- tsint at the

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Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

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Q: The derivative I of the parametric equations and y=5vt is

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Q: find a parametric equation for the line that is perpendicularto the graph of the given equation at…

A: We have to find parametric equation for the line that is perpendicular to the graph of the given…

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A: The given equation of circle at (a,0) is The general parametric equation of circle is where x,y…

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

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Q: s) Find the parametric equations of the line that is perpendicular to the plane 2x +y+3z = 4 through…

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

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

A: Let's find.

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + 4y +…

A: Equation of line normal to graph of functions f(x) is :  r<t> = <x0,y0,z0> +…

Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

Q: Find the First and Second derivatives of y with respect to x from parametric equations. a). x=3 (t…

A: x = 3 t + 22   and y = 9 t2 - 5⇒dxdt = 3 ×2 ×( t + 2)  , dydt = 18 t        Hence dydx = 18 t 6 ( t…

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 a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

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

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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: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

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Q: Find the points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which the…

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Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = t3 +…

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Q: Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2)…

A: First differentiate x and y wrt t then divide

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x+2y…

A: Let F(x,y,z) define a surface that is differentiable at a point (x0,y0,z0), then the normal line to…

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

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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: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: Eliminate the parameter in x = -t +2t and y =t-4 and then identify the parametric curve and sketch…

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Q: 2. Find parametric equations for the tangent line to the curve r(t) = (t8,t³,t7) at (1,1,1).

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

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Q: find parametric equations for the given curve. 4x − y2 = 5

A: Given curve is:

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y² = 8 ,…

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