Find the curvature of the parametric curve: 元 끼리 x= [sin (±²²³) 40, y = {con (± 20³) 40. do, COS

Find the directrix of the parabola r = 25/(10 + 10 cos θ)

Write three different sets of parametric equations for the curve $y=\sqrt{x}$

Graph the curve with parametric equations x = sin(t), y = 2 sin(2t), z = sin(3t). And Find the total length of this curve correct to four decimal places.   Calculus 3

Differentiate the following hyperbolic functions.

Find the point-slope equation of the tangent line to the parametric curve given by x = 1+ 2t and y = -1– 2t at the point (-1, 1).

Consider the parametric curve defined by x = 2020 cos t y = 2020 sin t TC Find the slope of this curve when t = 3 -1010V3 -V3 v3 V3 O 1010

Find the equation of the curve whose parametric equations are x = 1 + 4 cos 0, y = 2 + 3 sin 0, 0 € R.

Use the parametric equations x= sec(t) , y=tan(t), for -pi/2 < t < pi/2. Sketch the curve represented by the parametric equations (include the orientation of the curve) and write the corresponding rectangular equation by eliminating the parameter and Find the equation of the tangent line to the curve at t = pi/4

4. Eliminate the parameter and write the parametric equation in rectangular form x = 3 sece, y = 5 tan0