Give parametric equations that describe a full circle of radius R, centered at the origin with clockwise orientation, where the parameter varies over the interval [0, 10].

Q: Find three different pairs of parametric equations for the line segmentthat starts at (0, 0) and…

A: Direction ratio is = (6-0, 6-0)= (6,6) That is equivalent to (1,1) , (2,2) and (3,3)

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: 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: What are plane curves and parametric equations?

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

A: We should understand that y is going to be constant  and is going to be 3   Now since r = 2 [given]…

Q: Give a parametric description for a cone with radius a and heighth, including the intervals for the…

A: We can parameterise the same as following: Assume s & t as two parameters radius = a and height…

Q: Find the exact value of the number a so that the length of the curve defined parametrically by

A: We have been given the parametric curves and have to find the value of a constant a.

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

A: The graph of the parametric equation x=t+2, y=t can be plotted as the following.

Q: By eliminating parameter t, sketch the parametric curve for the given parametric equations. Then,…

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Q: Give a parametric description for a cylinder with radius a andheight h, including the intervals for…

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Q: Sketch and identify the curve defined by the parametric equations x = sin²t, y = 2 cost

A: Given the parametric equations  x=sin2t y=2 cost To find : Sketch and identify the curve using given…

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

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

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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 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: find parametric equation (cartesian) for tagent line to r=cos(2theta) at theta=2

A: The equation of the tangent line is

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: Use parametric equations to derive the formula for the surface area of a sphere of radius a.

A: We know that parametric equations of the sphere, x=acosθsinϕy=asinθsinϕz=acosϕ So parametric vector…

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

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Q: Find parametric equations for a circle of radius 2, centered at (3, 5).

A: Solution:Given    radius of the circle=r=2centre of the circle(h,k)=(3,5)To find the parametric…

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

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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: 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: 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: Find parametric equations for the circle x2 + y2 = a2, using as parameter the arc length s measured…

A: The given equation of circle is,

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

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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 an equation of the circle with center at (-4,1) that is tangent to the y-axis in the form of…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

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: Give a parametric description for a sphere with radius a, includingthe intervals for the parameters.

A: We will use the spherical coordinates for parametrization. Where ρ= radius= a And,

Q: A circle is specified in parametric form by x=7+3cosθ y=−8+3sinθ What are the coordinates of the…

A: Given : A circle is specified in parametric form by  x=7+3 cosθy=-8+3 sinθ To Find : What are the…

Q: Two parametric equations are given by: x = cos (1), y sin (t) u- sin(t) v - cos(t) In one figure,…

A: Any point in the cartesian coordinate system is defined as x,y. The parametric functions are defined…

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 for the given curve. Circle of radius 4 with center (3, 9)

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

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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 tangent line to the curve of intersection of the following two…

A: We have to find parametric equations for the tangent line to the curve of intersection of the given…

Q: Find the length of the latus rectum of the curve r = 2/(1 - cos( theta )) in polar coordinates.

A: Given r=21-cosθ

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: find parametric equations for the given curve. Segment joining (1, 1) and (2, 3)

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Q: Find parametric equation of a helix radius 5 from a point (5, 0 ,0) to a point (0, 5, 1)

A: Given that the radius of the helix is R=5. We know that the parametric equation of helix is given…

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: 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