Identify the surface defined by the following equation. x2 +y2 + 32- +6x= -8 Select the correct choice below and fill in the answer boxes to complete your choice. O A. The surface defined by the equation is an ellipsoid centered at that has length in the x-direction, in the y-direction, and in the z-direction. O B. The surface defined by the equation is an elliptic cone centered at and whose traces in the xy-plane are ellipses. O C. The surface defined by the equation is a hyperboloid of one sheet centered at and is centered around the z-axis. In the xy-plane, the trace has length in the x-direction and length in the y-direction. O D. The surface defined by the equation is a hyperboloid of two sheets centered at and whose traces in the xy-plane are ellipses. The shortest distance between the two sheets isFind a function r(t) that describes the line passing through P(4,3,5) and Q(8, 7,2). r(t) = (4t + 4, 4t + 3 , 13t+ 5 , for -00Find the point (if it exists) at which the following plane and line intersect. 5x - 10y - 4z = 16 and x = - 2- 4t, y = -4-6t, z=2 - 3t Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. O A. The point at which the line intersects the plane is (Simplify your answers. Type an ordered triple.) O B. The line and the plane do not intersect.Identify the surface defined by the following equation. + 6x - 10y = 35 Select the correct choice below and fill in the answer boxes to complete your choice. O A. The surface defined by the equation is an elliptic cone centered at and whose traces in the xy-plane are ellipses. O B. The surface defined by the equation is a hyperboloid of two sheets centered at and whose traces in the xy-plane are ellipses. The shortest distance between the two sheets is O C. The surface defined by the equation is an ellipsoid centered at that has length in the x-direction, in the y-direction, and in the z-direction. O D. The surface defined by the equation is a hyperboloid of one sheet centered at and is centered around the z-axis. In the xy-plane, the trace has length in the x-direction and length in the y-direction