Find a set of parametric equation to represent the graph of y=x^2 + 2parameter a) t =x b) t=2-x Find a set of parametric equation to represent the graph of y=x^2 + 3 parameter a) t=x^2 -2 b) t =4x

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 a set of parametric equations of the line with the given characteristics. The line passes…

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Q: Find a set of parametric equations of the line passes through the point P (1, 2, 3) and parallel to…

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Q: What are parametric equations in two variables? How does the definition generalize to parametric…

A: A pair of variable (x,y) is said to parameterized if they are represented as a function of other…

Q: What are plane curves and parametric equations?

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Q: Sketch the curve represented by the parametric equation and indicate the orientation of the curve.…

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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: A pair of parametric equations is given. x = cos(t), y = cos(2t) (b) Find a rectangular-coordinate…

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Q: Find parametric equations for an object moving clockwise along the ellipse = 1 beginning at (0,2)…

A: To find out the parametric equations for the given.

Q: Use a graphing utility to graph the curve represented by the parametric equationsHypocycloid: x = 3…

A: Given Data The first equation of hypocycloid is x=3 cosᶟθ. The second equation of hypocycloid is y=3…

Q: What is a cycloid? What are typical parametric equations for cycloids? What physical properties…

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Q: Find parametric equations for the circle of radius 2 with center (1, 1). Use the equations to find…

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Q: Find a set of parametric equations of the line with the given characteristics. The line passes…

A: Given: Point (-6, -8, 2) and plane: xz-plane  To Find: Set of parametric equations of the line…

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: 1 Find parametric equations for the path taken by a point the distance between the centre and the…

A: The given question has been solved in detail

Q: 10) (section 10.7) Find parametric equations for a circle centered at ( 5,6) with a radius of 4 and…

A: Given:

Q: Find the parametric equations of the intersection of the planes x + (y - 3) + z = 0 and -x + (y + 3)…

A: Definition used -               Cross product of two vectors a→ =a1i+a2j+a3k,  b→ =b1i+b2j+b3k…

Q: Find a set of parametric equations of the line with the given characteristics. The line passes…

A: we know that parametric equation of line which passes through given point r0x1,y1,z1 and have…

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: The path of a projectile that is launched h feet above the ground with an initial velocity of v0…

A: x=100 cos 40t=76.6t and y=6+100 sin 40t-16t2=6+64.3t-16t2 describe the position of the ball as a…

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

A: The general parametric equations for circle which has center at (0,0) and radius R orientated 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 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: find parametric equations for the lines with the given description.  Passes through (1, −1, 0) and…

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Q: Which set of parametric equations represents the curve shown in the figure?

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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 a set of parametric equations of a circle centered at (2,3) with a radius 2 generated clockwise

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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: . 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: Curtate cycloid: x = 20 – sin 0, y = 2 – cos 0 -

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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 through (-4,1,1) parallel to the x-axis. Let z = 1. y-z=…

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Q: Let line 1: x = = = and point P(1,0,1). 2 ● Find the set of parametric equations of the line…

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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: What is the rectangular equivalence to the parametric equations? x(θ)=2sinθ+1,y(θ)=3cosθ−2 , where…

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Q: Find a set of parametric equations for the line passing through the point (7, 0, 2) that is parallel…

A: We are asked to find the equation of the line.

Q: An ant is walking around an ellipse (as seen below). The ant starts at the top and walks around in a…

A: Given: An ant is walking around an ellipse. The ant starts at the top and walks aroundin a clockwise…

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: 5. A rock is tossed from a height of 2 meters at an initial velocity of 30 m/s at an angle of 20°…

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Q: Prolate cycloid: x = 20 – 4 sin 0, y = 2 –- 4 cos 0

A: We have that the curve is smooth when x' and y' are continuous on an interval I and x' and y' are…

Q: A circle of radius 1 rolls around the outside of a circle of radius 2 without slipping. The curve…

A: Radius of fixed circle a=2 Radius of rolling circle b=1 ∠ICP=φ   aθ=AI=PI=Bϕ…

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

A: Given parametric equations

Q: Select two different sets of parametric equations for the rectangular equation. 7 y =

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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: x = sec 0 y = tan 0

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