Eliminate the parameter in x = -t^2+9t and y = t-4 and then identify the parametric curve and sketch it's graph.

Q: Find the length of one arc of the curve whose parametric equation are x=2θ-2sinθ and y=2-2cosθ.

A: We have to find length of arc whose parametric equations are : x=2θ-2sinθ and y=2-2cosθ Suppose 0 ≤…

Q: Identify the variables in the following parametric equations modeling projectile motion: x =…

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y² – 9z2 = 4, (-2, -3,…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

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: Which indicates the derivatives of parametric equations? *

A: Solution: Option D Derivatives of a Parametric function:  x = g(t) and y = f(t)  dxdt= g'(t), dydt=…

Q: What is the equation of the curve described by the parametric equations x = 3+cost,  y = -5+sint ?

A: What is the equation of the curve described by the parametric equations x = 3+cost,  y = -5+sint ?

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: Find parametric equations and a parameter interval for the motion of a particle that starts at the…

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Q: Find the parametric equations for the tangent line to the curve

A: Here we have to find the parametric equations for the tangent line to the curve,  x=t3-1, y=t2+1,…

Q: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

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Q: Find parametric equations for the surface generated by revolving the curve y = 1/x about the x-axis.

A: When y = f(x) is rotated about x axis, we get a surface with parametric representation is,…

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

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Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost 0≤…

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Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 - 4t +…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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

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Q: (a) How do you find the slope of a tangent to a parametric curve?

A: (a) Assume a general parametric curve. Differentiate and find the derivatives.

Q: Cannot solve

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Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost…

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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 the equation of the tangent line to the parametric curve x = 2t2 and y = 7t2 – 2t3 – 1 at the…

A: find the slope of function using the chain rule and then use the equation  of a tangent line to…

Q: By eliminating the parameter, determine the rectangular equation equivalent to the parametric…

A: This is the problem of the application of differential calculus and parametric to cartesian…

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

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Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Graph the parametric curve x=2t-3, y=6t-7 by

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Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 – 4t +…

A: We find out dy/dx .then we find out value of t at given points and then find slope of tangent line…

Q: find a parametrization for the curve. the line segment with endpoints (-1, -3) and (4, 1)

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Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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Q: How might the parametrized curve differ from the graph of its Cartesian equation?

A: Graph: In Cartesian equation you represent curve as a direct relationship between x, y coordinates.…

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

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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: Convert x = = ln(2t) and y = 1² from parametric to rectangular form. 2

A: Given,  x=ln(2t) and y=12t2

Q: Distinguish briefly the Parametric and non-parametric analysis

A: There are two types of analysis in the testing of the hypothesis. they are: 1) Parametric analysis.…

Q: of the points where the parametric equation y = 3 cost 0≤t≤ 2T will have a horizontal tangent.…

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Q: find parametric equations for the given curve. Circle of radius 4 with center (3, 9)

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Q: Find parametric equations for the line segment thatgoes from Q(0, 3) to P(-2, 0).

A: Given Q(0,3) and P(-2,0)

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

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Q: Find an equation of the tangent plane to the given surface at the specified point. 5Vy Z = (-1, 1,…

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Q: Draw the curve given by the parametric equationsx=t3+t2−t,y=t3+2t2−4t.

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Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?

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Q: 2. Find the SA generated by rotating the first quadrant portion of the curve y = 9- x2 about the…

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Q: Determine the parametric equations of the path of a particle that travels the circle:

A: Given,        (x-4)2+(y-3)2=49 Time interval is 0≤t≤2π

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: Under what circumstances can a graph that represents a set of parametric equations have more than…

A: On considering the parametric equations x=f(t) ----(1) y=g(t)----(2) Where, x and y is a function…

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

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Q: Let L be the line with parametric equations

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