Saddle surface of a hyperbolic paraboloid / Models // Mathematical Etudes

Elliptic Geometry | Definition & Applications

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

Paraboloid: Definition

The paraboloid is formed by revolving the shaded area around th... | 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