2. (parametric curves) Find a parametric equation for the following curve using 0 as the parameter and (0, 0) as the terminal point: 0 y = √x (x, y)

find the parametric equations for the line segment from (-2,5) to (7,-1) your equation for x should not be x=t. define your interval for the parameter t.

Find a parametric equation for the line that is perpendicular to the graph of the equation 2x² + 3y² + 3z² = 47 at the point (2,3,2).

find a parametric equation for the line that is perpendicularto the graph of the given equation at the given point. x2 + y2 + z2 = 14, (3, -2, 1)

Find parametric equations and a parameter interval for the motion of a particle that starts at the point (-2, 0) in the xy-plane and traces the circle x2 + y2 = 4 three times clockwise.

find parametric equations for the line tangent tothe curve of intersection of the surfaces at the given point. urfaces: x2 + y2 = 4, x2 + y2 - z = 0 Point: (√2, √2, 4)

Consider an astroid with parametric equations x=4cos3(t),y=4sin3(t)     (a) Find the slope of the tangent line to the astroid in terms of t. Slope =    (b) List all of the points (x,y) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of x. If two or more points share the same value of xx, list those points starting with the smallest value of y. If any blanks are unused, type an upper-case "N" in them. Point 1: (x,y)= ( , ) Point 2: (x,y))= ( , ) Point 3: (x,y)= ( , )   (c) List all of the points (x,y) where the tangent line is vertical. In entering your answer, list the points starting with the smallest value of xx. If two or more points share the same value of xx, list those points starting with the smallest value of yy. If any blanks are unused, type an upper-case "N" in them. Point 1: (x,y))= ( , ) Point 2: (x,y)= ( , ) Point 3: (x,y)= ( , )   (d) List all of the points (x,y)(x,y) where the slope of the tangent line is…

Sketch the plane curve represented by the given parametric equations x = t2 + t + 1, y = 2t. Then use interval notation to give relation’s domain and range.

Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C, defined by the parametric equations x=9vt-2, y = 3t² - t³, at the point (-9,2).

What is the parametric equation for the line tangent to the curve C, with the equation:   at (0,1)