Show that the parabola y = ax2, a ≠ 0, has its largest curvature at its vertex and has no minimum curvature. (Note: Since the cur-vature of a curve remains the same if the curve is translated or rotated, this result is true for any parabola.)

Q: Find the curvature k of the curve C : 16 =1 at the point (0, 3)

A: 1. convert the equation into parametric form 2. use formula for curvature written below

Q: Find the curvature of the parabola given byy = x −(1/ 4)x2at x = 2. Sketch the circle of curvature…

A:

Q: Find the curvature of y = sin(3T) at a = =.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 04. Show that the Gauas and mean curvatures on, X-(u+v,u-v, uv) at u=1, v=1 are K=1/16 and H= JI.…

A: Given: 1) X=(u+v,u-v,uv) at u=1,v=1. 2) The paraboloid is xy=aZ.

Q: Find the curvature and radius of curvature of the plane curve at the given value of x . y = x −4/ x,…

A:

Q: 2. Show that if a : [a, b] → R" is a regular parameterization of a curve then the curvature at α(t)…

A: Let, is a regular parameterization of a curve. To show the curvature at  is .

Q: Find the curvature and radius of curvature of the plane curve at the given value of x.

A: We have,   It is known that radius of curvature is given as, Here K is curvature of the curve.…

Q: Determine the maximum curvature for the graph of f(x) = 6 In (3x). The maximum curvature is at x =

A:

Q: Find the curvature and radius of curvature of the parabola y=x2 at the origin.

A:

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x - 32 ,…

A:

Q: Find the curvature k of the curve C : 16 = 1 at the point (4, 0)

A: Curvature K of curve is : -16/3

Q: Show that the regular curve a = a(s) is a straight line if and only if its curvature k is dentically…

A: WE HAVEDB/DS = τNWHERE AT ANY POINT P[X,Y,Z] ON THE CURVEB IS UNIT VECTOR CALLED BINORMAL TO THE…

Q: Show that along the plane curve x = #1(t)e, +2(t)e2 the curvature is 4.30. [(a)2(5)213/2 a0 + 3

A: The curvature K at a point of a curve defines the speed of rotation of the tangent of the curve at…

Q: In Exercises 27 and 28, determine the maximum curvature for the graph of each function. 27. ƒ(x) =…

A: The curvature of a function is given by the following formula.

Q: Q2 Find the radius of curvature of yv5 = x' at the point (x, y,). Hence, show that the radius of…

A: Use formula of radius of curvature

Q: Suppose I → R³ is a regular curve -c3 with zero curvature anywhere zero, and then the H-curve holds…

A: A given regular curve with zero curvature is -c3 We change in terms of t, then the regular curve is…

Q: Find the curvature K of r(t)= 2ti +t²j - k 3

A: We know that, the expression for the curvature; kt=r→'t×r→''tr→'t3 Given r→t=2ti→+t2j→-13t3k→

Q: 2-Show that the regular curve a = a(s) is a straight line if and only if its curvature k is…

A: Here we have to show that a regular curve is a straight line if and only if, its curvature is…

Q: 138. At what point does the curve y = e* have maximum curvature?

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Find the curvature k of the curve C: 16 =1 at the point (4, 0)

A: Given The curve C : x216+y29 = 1  We have to find the curvature κ of the curve at the point 4, 0.

Q: Find the curvature of the curve r (t) = (- 5+ 4t, 1+ 3t, 5t) at the point t - 7.

A:

Q: Find the curvature of the curve r(t) = 3ti + 2t2j at the point P(−3, 2) .

A: rt=3ti+2t2j Comparing with rt=xi+yj, we get x=3t & y=2t2 Now put x=-3 & y=2, we get -3=3t…

Q: 1. Find the points on the parabola y 8x at which the radius of 125 curvature is 16

A:

Q: Find the curvature k of the curve given by r(t) = (2t²,t, ¿ť²)

A:

Q: The curvature of y =x is

A: In this question we have to find the curvature of the given function which we can find out by using…

Q: Find the curvature of r(t) = at the point (1,0,0)

A:

Q: Find the y coordinate of the center of curvature of th parabola at (2,2).

A:

Q: Consider the curve given by the equation y2+x3=0. Find its curvature at the point (−1,1).

A:

Q: Find the center of curvature of the curve y=Inx at (1, 0). A) (4, 3) (в) (3,4) c) (3, -2) D (-2, 3)

A: Ans D

Q: Find the curvature of a superellipse defined by the parametric equations…

A:

Q: Given the curve f (t)= (2t2 - 3, 3 - t, 3 + 2t?). Find the equation of the line parallel to the…

A: Consider the equation as shown below: Here, curve ft =2t2-3, 3-t, 3+2t2 Here, the object is to find…

Q: If a chord of the parabola y? = 4ax is a normal at one of its ends, show that its mid-point lies on…

A:

Q: Show that the parabola y = ax2, a  0, has its largest curvature at its vertex and has no minimum…

A:

Q: 10.) At what point does the curve have maximum Curvature? y=In(x). K(x)= f"|

A: firstly find f, f' and f'' . And substitute all these values in given curvature formula.  After that…

Q: Find the y coordinate of the center of curvature of the parabola at (2,2). 7. -7 -6 6.

A:

Q: Find a plane curve a(s) endowed with a unit-speed prametrization by SE (-0, 0) such that its signed…

A: The curvature of the curve αs is given by: αs=∫s0scos(θ(u))du, ∫s0ssin(θ(u))du-----(1) in which…

Q: Find the curvature k of the curve C: 16 + =1 at the point (0, 3)

A: To find the curvature of the curve at the point (0,3).

Q: Show that the Gauas and mean curvatures on , X = (u + v,u –- v,uv) at u = 1, v = 1 are K = 116 and H…

A: Given, X=u+v,u-v,uv u=1,v=1 , k=116 and H=182 We know that, E=xu,xuF=xu,xvG=xv,xv So, we need to…

Q: Find the point on the curve y = (x − 8)² +9 at which the curvature K is a maximum.

A:

Q: 8) If curvature of a space curve at (2,3) is 8 and curvature at (7,1) t=7 is 1, what can be said…

A: Given that curvature of a space curve at 2,3 is 8 and curvature at 7,1 is 1.

Q: If 7(t) = then the curvature at the point (2,0,0) is

A:

Q: Find the gaussian and mean curvature functions of the surface m given by the equation y3=y1y2 in R³…

A: First parameterized the equation.

Q: Show that the ellipse x = a cos t, y = b sin t, a> b>0, has its largest curvature on its major…

A: The curvature for a parametrized curve c(t) = x(t)i + y(t)j is :

Q: Find the curvature K(t) of the curve

A:

Q: At what point does the curve have maximum curvature? y = 7 In(x) (x, y) = What happens to the…

A: Given,              y = 7 ln(x)

Q: Consider the plane curve parametrized by F(1) -i+ (In(com(1)J, Find curvature s(4).

A:

Q: The curvature of y = x2

A: so we have to find curvature of y =  x2. we use the formulae for curvature  k(x) =…