Find an equation for the projection of the curve on xy plane. (Hints: First, figure out from which point does the curve start. Do not forget that we consider only t > 0.) y=x y = x3 O y = x³; x 2 0 O x = y°; y 2 0

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Q: x = t + t and y = t* + 2t²

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Q: In what plane does the curve r(t) = t i + t2 k lie?

A: r(t) = t i + t2 k We need to find the plane of the curve located in?

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Q: The cartesian equation of the curve x = vt ,y= 1– t is : (a)y = 1 – x², x 2 0 (b)y = 1 – x ,x 2 0…

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Q: Consider the following. x = et - 4, y = e2t (a) Eliminate the parameter to find a Cartesian equation…

A: To find The cartesian equation of the curve by eliminating the parameter

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A: First eliminate t then solve

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A: Given parametric equation is  x=lnt, y=t,       t≥81

Q: 4. Find a parametric form of the curve given by 2r + 3y? - 6r + 6y + = 0 in the ry-plane with a…

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Q: The cartesian equation of the curve x = 1-t,y= t is : (a)y = 1– x², x20 (b)y =1-x ,x 2 0 (c) x = 1 –…

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Q: The parametric equations of a curve are x = and y = t³ + 4 – . Given = -;(t* + 1). Find the value of…

A: The parametric equations of curves are x=6t, y=t3+4-3t   Given dydx=-12t4+1 We have to find that…

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A: Given:-paametric equation:x=t y=1-tsince we have to find the cartesion equation

Q: Consider the following. x = e3t,    y = t + 8    (a) Eliminate the parameter to find a Cartesian…

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Q: Evaluate given that F (7, y) = 2yî + (zy – 2r)j and Cis the curve in the third quadrant from the…

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Q: The position P(x, y) of a particle moving in the xy-plane is given by the equations and parameter…

A: Given data:     The given x-coordinate in parametric form is: x=t1/2. The given y-coordinate in…

Q: Consider the following. x = t4, y = In(t) (a) Eliminate the parameter to find a Cartesian equation…

A: We have to find the Cartesian equation

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

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Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

A: The given differential equation is dydx=3x, y(0)=-3

Q: The cartesian equation of the curve x= vt ,y =1-t is : (a)y = 1– x², x 2 0 (b)y =1-x ,x20 (c) x = 1…

A: Eliminate t in given equation.

Q: Consider the following. et – 6, y = e2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given that

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A: parametric equations x=3cos(2pi t)+2, y= -6cos(2pi t)+1.

Q: The cartesian equation of the curve x= vt ,y 1-t is: (a)y = 1– x2, x2 0 (b)y = 1-x,x N0 %3D (c) x =…

A: Eliminate t then solve

Q: x = et – 1, y = e2t a) Eliminate the parameter to find a Cartesian equation of the curve.

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Q: (c) (d) Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain…

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Q: s on the graph of parametric equations 2VE %3D tF (2,0), then |PF|= B. 5 C. 6 D. 7

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 3. he tangent to the ellipse I at the point P: V2 4. 3. 3w q(w) = 2w+ V2 %3D 3 q(w) = 3w V2w - V2 3…

A: Ellipse tangent

Q: Find the equation of the curve at any point  P(x,y) of a curve the subtangent equals -1/x

A: Given that the subtangent equals -1x. Then we get, tan θ2=-1x⇒tan θ=2 tan θ21-tan2 θ2⇒tan…

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Q: The cartesian equation of the curve x= f ,y = 1-t is : (a)y = 1– x², x 20 (b)y =1-x ,x 2 0 (c) x = 1…

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Q: Please answer this as soon as possible. I badly need the correct answer. Thank you. Find the…

A: The given family of curves are                                          y2=x2(1-cx)

Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: The cartesian equation of the curve x = vE .y 1-t is: (a)y = 1- x2, x 2 0 (b)y = 1-x ,x 20 (c) x =…

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Q: The cartesian equation of the curve x = 1-t,y= vt is : (a)y = 1- x2, x 2 0 (b)y = 1 - x ,x 2 0 (c) x…

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Q: A curve has an equation of 9x2 + 25y2 = 225. Compute the second eccentricity of the curve. %3D 1.33…

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Q: The cartesian equation of the curve x = 1-t.y vt is: (a)y = 1-x, x2 0 (b)y = 1-x .x 20 (c) x=1-…

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Q: (C) Find parametric equations for the line that is tangent to the curve u(t)=1²1+ sect²j+ √² +3 k at…

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Q: Find the parametric equation for the line where the planes 4x – 6y + 8z = - 36 and – 6y + z = – 15…

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric curve is, x=2ty=8t3-1≤t≤1 From the parameter of x, x=2tt=x2

Q: Consider the following. x = et, y=e-2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given  x=et  ,  y=e-2t   Then we can find out cartesian curve by eliminating parameter 't' .

Q: 2. Find T, N, and x, the center of the osculating circle, the equations of the osculating,…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: x = et – 3, y = e2t (a) Eliminate the parameter to find a Cartesian equation of the curve.

A: As per company guidelines, I'm restricted to answer your first question only. So if you want other…

Q: Eliminate the parameter to find a cartesian equation of the curve  x=e^6t-5, y=e^12t

A: It is given that,

Q: Find 2 for the parametric curve c(t) = (3r³, 3r² – 3) at the point t = 4. (Use symbolic notation and…

A: Consider the parametric curve  ct=3t3,3t2−3 To find : dydxt=4

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.