Eliminatetheparameter. Find a retangular equation for the plane curve defined by theparametricequations. X=3t, y=t+7
Find a set of parametricequations for the rectangular equation. Y=2x-2

Findtheparametricequations for the path of a particle that moves along the circle
x^2 + (y-1)^2 = 4
as follows:
(a) Once around clockwise, starting at (2,1);
(b) Three times around counterclockwise, starting at (2,1);
(c) Halfway around counterclockwise, starting at (0,3).

Following are the instructions from my teacher for the final review. please follow directions precisely and show all steps by hand. Answers must be exact unless otherwise indicated.
1) Consider theparametricequations x =2t+1/t and y = 1-t.
(i) Using a table sketch the curve represented by theparametricequations. Writ

1,2,3) a) Sketch the curve by using the paramtric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
b) Eliminatetheparameter to find a cartesian euqation of the curve.
1)x = 3t-5, y=2t + 1. Part a is just making a table using t and solving for x and y, but whe

1. Rotate the coordinate axes x and y by the appropriate acute angle theta, so as to eliminatethe cross product term (xy) from the equation x^2 + xy + y^2 - 6 = 0. State the value of theta, give the transformed equation in terms of the new rotated coordinates u and v, and identify the figure it represents.
2. Findcartesian

You are given the vectors
X = (1,1,1), y = (2,1,1) and z = (6,2,2).
(i) FindtheCartesian equation of the plane Π normal to the vector x containing the point (2,1,1).
(ii) Findtheparametric equation of the line l through the points (2,1,1) and (6,2,2).
(iii) If l' is given parametrically by l' = x + ty (with x

Hello,
I am in a fast-paced Calculus course where I must learn new concepts each week; I find it challenging to grasp the concepts while remaining on-pace and I am experiencing great difficulty. I am really finding it difficult to grasp the concept of Parametric & Rectangular Equations, Slope & Concavity, and Tangent Lines.

Consider the set of points (x, y, z) defined by the set of equations below:
{ x = 1 - t }
{ y = 2t }
{ z = 1 + t }
where t is a real number parameter.
Find a 2 x 3 system of linear equations having this set of points as its solution set.
Please show all steps in your work and explain your answer in detail.