point) Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of one sheet elliptical cylinder; or a parabolic cylinder; and identify the axis of symmetry as the X-axis, the Y-axis; or the Z-axis 8x2 4y2 22 = 1along the X-axis along the y-axis along the z-axis9x2 8y2 z = 06y2 622 = 1 2x2 8y 22 = 08y2 9x2 8z2 1 = 0

Volume of a paraboloid The volume of a segment of a circular pa... | Filo

An immovable paraboloid (which was produced by rotating a parab... | Filo

The paraboloid z = 7 - x - x^2 - 2y^2 intersects the plane x = 3 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (3, 2, -13). Use a computer to graph the paraboloid, the parabola, and the tangent line on the same screen. (Enter your answers as comma-separated lists of equations. Use t as your parameter.)

Show that if the point (a, b, c) lies on the hyperbolic paraboloid z=y^2-x^2, then the lines with parametric equations x=a t, y=b t, z=c 2(b-a) t and x=a t y=b-t, z=c-2(b a) t both lie entirely on this paraboloid. (This shows that the hyperbolic paraboloid is what is called a ruled surface; that is, it can be generated by the motion of a straight line. In fact, this exercise shows that through each point on the hyperbolic paraboloid there are two generating lines. The only other quadric surfaces