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- Find the equation of the ellipsoid passing through the points (+5,0, 0), (0, ±6, 0) and (0, 0, ±7) = 16. The ellipsoid 4x2 + 2y? + 22 = 16 intersects the plane y = 2 in an ellipse. FInd parametric equations for the tangent line to this ellipse at the point (1, 2, 2).Determine the greatest and least distance from the origin to a point on the ellipsoid 9x2+4y2+z2=36
- 3. Write the equation + + 1 = z in (a) cylindrical coordinates and (b) spherical coordinates.The ellipsoid 5x2 + 2y2 + z2 = 81 intersects the plane y = 6 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 6, 2). (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.)6. Find the cylindrical equation for the ellipsoid 4x² + 4y? + z² = 1.
- Find parametric equations and a parameter interval for the motion of a particle in the xy-plane that traces the ellipse 16x2 + 9y2 = 144 once counterclockwise.Consider the following. The ellipsoid 2x² + 7y² + z² = 50 intersects the plane y = 2 in an ellipse. Find the slope of the tangent line to this ellipse at the point (3, 2, 2). -2 X Find parametric equations for the tangent line to this ellipse at the point (3, 2, 2).Convert z = 9x2 - 9y2 to cylindrical coordinates.
- Find parametric equations for an object moving clockwise along the ellipse (x2/25)+(y29)=1 beginning at (0,3) and requiring 4 seconds for a complete revolution.Consider the following. The ellipsoid 9x² + 2y² + z² = 98 intersects the plane y = 2 in an ellipse. Find the slope of the tangent line to this ellipse at the point (3, 2, 3). -3 Find parametric equations for the tangent line to this ellipse at the point (3, 2, 3). x=3+t, y = 2, z = 2 - 3t XFind parametric equations and a parameter interval for the motion of a particle in the xy-plane that traces the ellipse 16x2 + 9y2 = 144 once counterclockwise. (There are many ways to do this.)