Sketch the plane curve represented by the parametric equations x = Vi and y = 2t – 1 by eliminating the parameter.

Q: Sketch the plane curve represented by the given parametric equation x = t2 + t + 1, y = 2t. Then use…

A: Graph: The parametric equations are,x=t2+t+1y=2t We need to draw a graph:

Q: Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation: x (t) = –t =…

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Q: Determine A so that the curve y = 4x+ 16 can be written in parametric form as x(t) = t – 5, y(t) At…

A: Put value in given equation and simplify

Q: Write an equation in general form of the tangent plane to the parametric surface at the stated…

A: Equation of tangent plane

Q: Eliminate the parameter to write the parametric equations as a Cartesian equation. If x(t) = 3t – 2,…

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

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Q: Consider the parametric curve x = t², y = t, -∞ <t < o∞. Find the point (a, b) on this curve that…

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

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Stretch the curve given by the parametric equations: x = tcost, y = tsint, t ≥ 0

A: Curve sketch of x=tcos(t)  And y= tsin(t) is

Q: Consider the parametric equations below. x = 4 + 5t,    y = 1 − t2   Eliminate the parameter to…

A: Calculation:Compute the Cartesian equation as follows.Rewrite x = 4 + 5t as follows t = (x – 4)/5.

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

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Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = x² –…

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Q: Consider the curve C given in parametric equations as

A: In this question, we find the tangent line and normal line along with that we find the point where…

Q: Sketch the graph of the parametric equation. x=sec t , y=tan t

A: Square both the equations.

Q: Sketch the curve x = 3sin?t, y = 4cos?t (0<t <÷) by eliminating the parameter, %3D and indicate the…

A: Introduction: When a function y=fx can be expressed as x≡xt,y≡yt by introducing a new variable t,…

Q: Sketch the curve represented by the parametric equations x = t + 1, y = t2 (indicate the orientation…

A: Given: x=t+1, y=t2. first we eliminate t and find equation of curve in x and y x=t+1…

Q: Eliminate the parameter on t to write the parametric function as a Cartesian equation in y = form.…

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Q: Find a parametric equation for the curve of intersection of the cone x²+y² = z² and the plane x+2z =…

A: We have to find a parametric equation for the curve of intersection of the cone x2+y2=z2 and the…

Q: Find the inflection points of the curve defined by the parametric equations:x=t2,y=t+t3.

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Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

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Q: The curve defined by any parametric equations X = f(t), y = g(t) is always a function.

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Q: Sketch and describe the orientation of the curve given by the parametric equations. x = V7, y = 2t –…

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Q: Complete the parametric equations for the line where the planes – 8z – 2y – 5z = 0 and - 4x + 2y –…

A: Given: The planes are -8x-2y-5z=0 and -4x+2y-9z=0 To find the parametric equation xt, yt, zt

Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: Sketch the curve represented by the parametric equations x = t − 3,                  y = t/(t − 3)…

A: Given: x=t-3                                                  ..1y=tt-3…

Q: Consider the parametric equations below. x = t2,    y = t5   Eliminate the parameter to find a…

A: We will solve for t from y = t5

Q: Describe and sketch the parametric curve in R given by x = cos t, y = sin t, z = sin 2t

A: The general form of the parametric equation of the curve in three-dimensional space is given by…

Q: Complete the parametric equations for the line where the planes - 7x + y + 3x = 3 and 4x7y + z = 23…

A: Given two planes -7x+y+3z=3 and 4x-7y+z=23

Q: Find a set of parametric equations for the curve of intersection of the paraboloid r² + 4y² -z = 0…

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Q: Match the parametric equation with the corresponding plane curve displayed. Sx=47-5 y=16 130 104 78…

A: The given parametric equation is: x=4t2-5y=16t4

Q: x = 1 + 4t,    y = 3 − t2

A: Here we extract t from the 1st equation then put this into second equation.

Q: Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π…

A: Given  x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π

Q: a) Find the are length of the parametric curve x = B(t. sint), y = B(1+ cost), in the range 0 sts,…

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Q: Sketch the parametric curve and draw an arrow specifying the direction and eliminate the parameter…

A: 14) The sketch of the given parametric curve is obtained by substituting different values of t and…

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: Sketch the curve represented by the parametric equations Lindices Orientation of the curve), and…

A: Topic :- function

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

A: Given parametric equations, x=et,y=e3t+4 To find y.

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

A: Solution

Q: 12. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for…

A: The given parametric equations are,

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: Sketch the curve represented by the parametric equations x = e−t ,y = e2t − 1 (indicate the…

A: The given parametric equations of curves are: x = e^(-t) y = e^(2t) - 1 The graphs of these…

Q: Sketch the curve represented by the parametric equations x = 2t/2, y = t4+ 1 (indicate the…

A: Given parametric equation, x=2t2 and y=t4+1we have to write the corresponding rectangular equation…

Q: Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric…

A: The slope of the tangent to the curve: y=fx at x=a is f'a. The point-slope form of a line that…

Q: Sketch the plane curve represented by the parametric equations x = Vi and y = }t + 1 by eliminating…

A: The parametric equations are given by x=t   …1 and y=12t+1   …2 Take the square of the equation (1)…

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

A: Given a parametric equation,   x=t3                ...(1)  y=t22              ...(2)

Q: Eliminate the parameter to find the Cartesian equation for the given parametric curve. = vt +1, y =…

A: Cartesian equations is x^2 - y^2 = 2

Q: Sketch the plane curve represented by the parametric equations x = 5 cos t, y = 2 sin t, 0 ≤ t ≤ π…

A: x=5cost,  y=2sint Now,…

Q: Calculate the exact length of the curve given by the parametric equations below z(t) = e' - t, y(t)…

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Q: Sketch the curve given by the parametric equations x= t³ - 1 and y= t² + t.

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

A: Given parametric equation, x=t         ...(1)y=t-5       ...(2)