Sketch the curve represented by the parametric equations. Find the rectangular-coordinate equation for the curve by eliminating the parameter. x=4t^2,y=8t^3

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

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Q: What is parametric equation?

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Q: Consider the curve defined by the parametric equations X = cos t, y = 3sec t on the interval…

A: To eliminate t and find cartesian equation.

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: parametric

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Q: Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the…

A: Take different values of t from the given interval and then plot the corresponding points and…

Q: find a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

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Q: What are plane curves and parametric equations?

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Q: Find parametric equations for the curve x = 5(y - 1)(y - 2) sin y and then plot the curve using a…

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Q: eliminating the parameter t from the parametric equation x = 3 cost y = 3 sin t, find the…

A: First we square both given equation and then adding both and solve it.

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 curve with the given properties. The line passing through (4, 5)…

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Q: x=e"Cost = e"S int

A: Given: x=e-tcosty=e-tsint At t=0: x=1, y=0 Differentiating both with respect to t:…

Q: This is the problem  If a and b are fixed  numbers, find parametric equations for the curve that…

A: It is required to define the point P in a, b  and θ.

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

A: Given that, x=tan2θ, y=sec2θ

Q: 14. The curve represented by parametric equations x = 4cose and y 4sine is a

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Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

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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: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² = 4…

A: SOLUTION:

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: Sketch the plane curve represented by the given parametric equations Then use interval notation to…

A: Given Plane Curve equation in parametric form is     x=3t,   y=t2+t+5  Now, Plane Curve equation in…

Q: Sketch the curve resonted by the parametric equation. Indicate of the curve. Dlease Label…

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Q: Without using a calculator, sketch the parametric equations by eliminating the parameter. Indicate…

A: The given parametric equation x=4+2cosθ and y=-1+sinθ

Q: 4. Eliminate the parameter and write the parametric equation in rectangular form x = 3 sece, y = 5…

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Q: Without using a calculator, convert the parametric equations of a curve into rectangular form. No…

A: Given that parametric equation and convert this equation into rectangular form and State the domain…

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: Give parametric equations that describe a circle of radius R, centered at the origin with clockwise…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

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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: What is the equation of family of central conics with common foci and axis. Determine its orthogonal…

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

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Q: . Find the slope of the line tangent to the parametric curve x = 2cost and y = 2- cos²t for 0<t<n at…

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Q: (a) What is a parametric curve?

A: If  x  and  y  are continuous functions of  t  on any interval I , then the equations: x=x(t) and…

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

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Q: Find parametric equations for the line through (-4,1,1) parallel to the x-axis. Let z = 1. y-z=…

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Q: Cannot solve

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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: State the formula to find the Curvature of a curve in parametric form.

A: We will state the required formula.

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 line tangent to the curve of intersection of the surfaces at the…

A: The tangent line in the solution should be perpendicular to the normal vectors of the surfaces. The…

Q: parametric equations representing the given curve.  Line passing through (0, 2) and (3, 1)

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

A:

Q: This is the problem    If a and b are fixed numbers, find parametric equations for the curve that…

A: Let the coordinate of point P is (x,y). In the triangle OCD, sinθ=CDOCsinθ=yby=bsinθ Similarly,…

Q: Find the parametric equations of the line that is tangent to circle

A: Question (1) - Equation of circle - x2+y2 = 25Differentiating on both sides with respect to x -…

Q: A long suspension bridge 180 meters from end,has towers 60 meters tall,where suspension cables are…

A: Given : from the data given above  the graph of the parabola is:

Q: 3) (i) Eliminate the parameter to find a Cartesian equation of the curve. (ii) Sketch the parametric…

A: Our objective is to eliminate the parameters to find the cartesian equation of the curve and sketch…