Total marks 15པ་(i) Sketch the trace of the following curve on R2,(t) = (t2 cos(t), t² sin(t)),t = [0,2π].[3 Marks](ii)Find the length of this curve.(iii)[7 Marks]Give a parametric representation of a curve : [0,that has initial point (1,0), final point (0, 1) and the length √2.→ R²[5 Marks]Turn over.MA-201: Page 4 of 5

Answered: Total marks 15 པ་ (i) Sketch the trace…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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Please answer parts iv, v and vi
7) A parametric curve is defined by the equations x = 2t + 3 and y = }t – 2 for –1
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=4et,y=te2t,z=tet^2;(4,0,0) Solve x(t), y(t), z(t)
Consider the parametric the curve defined by the equations x = t² – 2t + 2 and y = t² + t. (a) The point on the curve where the tangent line has a slope of - is (x, y) = (b) The tangent line at the point (æ, y) = (2,6) is given by the equation (Choose A, or B, or C, or D from the list below.) A) y = x – - B) y = -x + 1 C) Y +1 D) y = x+ 5
A curve is given by the parametric equations x=t^2/1-t y=t+1 give an implicit equation in x and y which specifies the same curve
Determine any differences between the curves of the parametric equations. (a) x = t (b) x = cos(0) y = 9t + 8 y = 9 cos(0) + 8 (c) (d) X = et y = 9et + 8 x = e-t y = 9e-t + 8 Are all graphs the same? Therefore, the graphs Select--- v all the same. Select- By eliminating the parameters in (a)-(d), you get y = are Are the orientations and restricted domains the same? are not O The orientations and restricted domains are the same. O The orientations are the same, but some of the restricted domains are different. O The restricted domains are the same, but some of the orientations are different. O Some of the orientations and restricted domains are different. Which of the curves are smooth? (Select all that apply.) O (a) O (b) O (c) (d) O O O O
Consider the parametric curve given by x(t) t² + t y(t) = t³ + 3t² = } te [-π,5/4]. (i) Find the axis intercepts. (ii) Find the critical points. (iii) Characterise the turning points. (iv) Find the extreme points. (v) Sketch the curve ensuring the direction of motion is indicated and all major points (from (i)–(iv)) are labelled. (vi) Find the equation of the line tangent to the curve when t = 1.
Please answer parts iv, v and vi, considering the attached answers for i, ii and iii.
13. Consider the curve C given by the parametric equations x = 2-3cos t and y=3+2sin t, for-있("아. 2 dy as a function of t. (a) Find dx (b) Find the equation of the tangent line at the point where t=- (c) The curve C intersects the y-axis twice. Approximate the length of the curve between the two y-intercepts.
t (3) Sketch the graph defined by the parametric equations x = e' -t and y = 4e? for 0
Find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point. x = 1 Surfaces: x + y² + 2z = 4, Point: (1,1,1) Find the equations for the tangent line. Let z = 1-2t. X = =(Type an expression using t as the variable.)

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