Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the elliptical cylinder (x^2)/16 + (y^2)/25 = 1 with the surface z = (x^2)*y.
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Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the elliptical cylinder (x^2)/16 + (y^2)/25 = 1 with the surface z = (x^2)*y.
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- Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane −12x + 2y + 6z = 0.Find the parametrization of the curve defined by the intersection of the two surfacesy = x^2 − 3z^2 and x^2 + z^2 = 9, where x ≥ 0.Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 3x2 + 2y2 + 6z2 = 29 at the point (−1, 1, 2).
- Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 + y^2 = 1 which lies in the first octantFind a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented clockwise. The point (6.0) should correspond to t = 0Find a parametrization for the cylinder x^2 + y^2 = 4.
- Find a point on the ellipsoid x2 + 4y2 + z2 = 9 where the tangent plane is perpendicular to the line with parametric equations x = 2 − 4t, y = 1 + 8t, and z = 3 − 2tFind the curved surface area of the solid generated by revolving the part of the curve y=x² from (0,0) to (√6,6) about the y-axis.A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 4.90 s, it is at point (4.60 m, 5.00 m) with velocity (2.00 m/s)ĵ and acceleration in the positive x direction. At time t2 = 13.6 s, it has velocity (–2.00 m/s)î and acceleration in the positive y direction. What are the x and y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.
- Show that the line normal to the surface xy + z = 2 at the point (1, 1, 1) passes through the origin.Find a parametrization of the hyper-boloid of two sheets (z2/c2)-(x2/a2)-(y2/b2)=1A point moves along the curve of intersection of the paraboloid z=x^2+5y^2 and the plane x=3. At what rate is z changing with y when the point is at (3,-1,14)?