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Find the point on the sphere (x 21:2 + y2 + {2 5:12 =16 nearest to a. the xy-plane. b. the point ( 8,0;5). a. The point on the sphere nearest the xy-plane is{ I. II I). Determine the graph of the cylinder. x2 + yz = 1 Choose the correct graph of the equation. O A. O B. O C. N Z P y XSketch the ellipsoid given by the equation below. 4x2 + 9y2 + 972 = 36 . . . Which of the following is the correct sketch of the ellipsoid? O A. O B. O C.Sketch the cone given by the equation below. 16x2 + 972 = 9y2 Which of the following is the correct sketch of the cone? O A. O B. O C. N -N 14 X\fA barrel is shaped like an ellipsoid with equal pieces cut from the ends by planes perpendicular to the z-axis. The cross-sections perpendicular to the z-axis are circular. The barrel is 2h units high, its midsection radius is R, and its end radii are both r. Find a formula for the barrel's volume. Then check two things. First, suppose the sides of the barrel are straightened to turn the barrel into a cylinder o radius R and height 2h. Check to see if your formula gives the cylinder's volume. Second, suppose r= 0 and h = R so the barrel is a sphere. Check to see if your formula give the sphere's volume. Click the icon to view a picture of the barrel. Find a formula for the barrel's volume. Assume the equation of the original ellipsoid to be a Volume = - X Picture of the barrel Below is a picture of the barrel in the problem statement. R X -horUse a CAS to plot the surface. Identify the type of quadric surface from your graph. 8x2 =z2 - 3y2 Choose the best graph of the equation below. O A. O B. O C.A line passes through the points P( - 2,2, - 3) and Q( - 5,4,2). Find the standard parametric equations for the line, written using the base point P( - 2,2, - 3) and the components of the vector PQ. - . . Let z = - 3 + 5t. x = . y= [. z=_ (Type expressions using t as the variable.)Find parametric equations for the line through (6, - 4,7) parallel to the x-axis. Let z = 7. X= . y = 0.z - 00 = = 0o (Type expressions using t as the variable.)Find the equation for the plane through the point Po = (5,4,6) and normal to the vector n = 3i + 3j + 7k. Using a coefficient of 3 for x, the equation for the plane through the point Po = (5,4,6) and normal to n = 3i + 3j + 7k is (Type an equation.)Find the equation for the plane through the points Po( - 2,5, - 3), Qo (3,3,3), and Ro( - 5,0, - 1). Using a coefficient of 26 for x, the equation of the plane is (Type an equation.)Find the point at which the line meets the plane. x = 2 + 5t, y= - 3+ 6t, z = 3+ 2t; x+ y+ Z= - 11 The point is (x,y,z) = (Type an ordered triple.)