Find the lines of curvature of a surface x=cosu y=sinv z=v
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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Find the curvature and radius of curvature of the curve y=cosmx at a maximum point.What is the geometric interpretation of the geodetic curvature of a curve taken on the surface.(differential geomtry)
- What is the relationship between the curvature of a surface and its Gaussian curvature in the context of differential geometry?Find the curvature and the radius of curvature of the curve y = x + 5x2 – 2x3 at the origin (0,0).Find the angle of inclination x² + y² = 26, A 0 of the tangent plane to the surface at the given point. (1, 5, 3)
- Fhd the equation of the tangent plane and normal line to the surface z = 2+y at the point (1, 1,3).Write a formula for the curvature of a plane curve with equation y= f(x)Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the given surface at a point. 교à +zi=8, P(16, 1, 16) x 2 + z 2 =
- A parabola has an equation of y²=2x, compute the radius of curvature at point (2, 2)Consider the curve with parametric equations X = t³ t² +1 = у What is the general equation for the curvature of this curve? O a. 3t/(t² + 1) b. 6/(4t² +9) ³/2 (2t)/(t² + 3t+9) ³/2 O ○ d. -6/(4t² +9) ³/2 e. 6t²/(9t¹ +4t²)³/²The two surfaces x2 + y2 + z2 = 6 and 2x2 + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the angle between the tangent planes at the point(1,1,2). Also, find the tangent vector to the curve in which surface intersect?