A circle of radius 1 rolls around the outside of a circle of radius 2 without slipping. The curve traced by a point on the circumference of the smaller circle is called an epicycloid. Use the angle θ to find a set of parametric equations for this curve.

Q: The parametric equations: x = a a cos 0,y = a sin 0;0 ses 2n, define a curve called an asteroid

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

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

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A: Solution is given below

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Q: (a) A curve is defined by the parametric equations x = tan²0, y = sec 0, π/2 < 0 <T/2. Eliminate the…

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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.

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A: The given question has been solved in detail

Q: (1) In row 2, use parametric equations to plot a unit circle. 3 (2) In row 2, adjust the parameter…

A: Asked questions are solved.

Q: The parametric equation for the y-axis is:

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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: Sketch the curve represented by the parametric equations x = 6 cos θ, y = 6 sin θ (indicate the…

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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: Obtain the parametric equations of: An epicycloid curve described by a point on the circumference of…

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

A: x = 2+5 cost → x-25=cost    y = 3+2 sint → y-32 = sint  Square both equations and add them.…

Q: Sketch the curve represented by the parametric equations x = 3 cos θ,             y = 7 sin θ…

A: Given:  x=3cosθ                                                     ...1y=7sinθ…

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Q: x = 1 – t², y = t – 2, –2 <t< 2

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

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Q: If you are given parametric equations of a curve, what is the formula for finding its arclength?…

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

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Q: Suppose you have the parametric equations x = 4cos(6) y= 6sin( 6 ) %3D Eliminate the parameter and…

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Q: Which of the following sets of parametric equations correctly represents the curve above

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Q: Find a parametric description for the top half of the unit circle, oriented clockwise.

A: Given that, the top half of the unit circle is considered. The standard equation of a unit circle…

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: Find the parametric equa

A: Given, the line in ℝ3 containing the points P=(-2, 5, 4)  and Q=(-4, 1, 1).

Q: Find parametric equations for the circle with center(h,k) and radius .

A: Find parametric equations for the circle with center(h,k) and radius r.

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: 18. x = et, y = e2t - 1

A: Solution

Q: What curve is represented by the given parametric equations, show it on the graph including t, x =…

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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: Sketch the curve represented by the parametric equations x = t3, y = t2/2 (indicate the orientation…

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Q: Sketch the curve for each pair of parametric equations. 2=3 cos t, y=5 sin t

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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…

Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Circle:  x = h +…

A: x=h+r cosθ , y=k + sinθ

Q: Sketch the curve represented by the parametric equations x = √t, y = t − 5 (indicate the orientation…

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Q: Sketch the curve represented by the parametric equations x = et , y = e3t + 1 (indicate the…

A: Sketch the curve represented by the parametric equations x = et , y = e3t + 1 (indicate the…