Curvature of Plane Parametric Curves The curvature of a plane parametric curve x = f ( t ) , y = g ( t ) is given by κ = | x y . − y ˙ x ¨ | x ˙ 2 + y ˙ 2 3 / 2 where the dots indicate derivatives with respect to t . 47. Find the curvature of the curve x = t 2 , y = t 3 .
Curvature of Plane Parametric Curves The curvature of a plane parametric curve x = f ( t ) , y = g ( t ) is given by κ = | x y . − y ˙ x ¨ | x ˙ 2 + y ˙ 2 3 / 2 where the dots indicate derivatives with respect to t . 47. Find the curvature of the curve x = t 2 , y = t 3 .
Solution Summary: The author calculates the curvature of a plane parametric curve x=f(t),y=t
The parametric equations
x = x1 + (x2 – x1)t, y = Y1 + (Y2 - Yq)t
where 0 sts 1 describe the line segment that joins the points P,(x,, Y,) and P,(x2, Y2).
Use a graphing device to draw the triangle with vertices A(1, 1), B(5, 3), C(1, 6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comm
separated list of equations. Let x and y be in terms of t.)
A to B
B to C
A to C
Find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point.
Surfaces: x+ y + 2z = 3,
X= 0
Point:
(0,1,1)
Find the equations for the tangent line. Let z =1- 2t.
How to generate the curve over the interval for the parameter t then find the equivalent rectangular equation?
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