Starting from the point (0, 4, -2) reparametrize the curve r (t) = (0 – 2t) i + (4 – 2t) j + (-2 + 0t) k in terms of arclength.

Q: Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y –…

A: The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

Q: Find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is…

A:

Q: Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3,…

A:

Q: Find the points on the curve 5x + 5y? - 6xy - 6xy = 4 nearest to the origin.

A:

Q: Find an equation for the line that is tangent to the curve y=x3 −9x at the point (3,0).

A: Given: The given curve is y=x3-9x and the point 3,0. To find: The main aim is to find the equation…

Q: Evaluate y' at the point (2,2) 5x3y - 2x2 = 72

A: The given equation is 5x3y-2x2=72. Rewrite the above equation as follows:…

Q: Find the point on the curve y = √x closest to the point (2,2)

A: Here we have to find the point on the curve y = sqrt (x) closest to the point (2, 2)   use the…

Q: Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every…

A: integration

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.

A: