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The basic way to identify the equation of hyperboloid of two sheets is to convert the given equation in one of the above forms and the main property of this equation is the two terms on the left ... • Equation • Types of surfaces – Ellipsoid – Hyperboloid of one sheet – Hyperboloid of two sheets – Elliptic paraboloid – Hyperbolic paraboloid – Elliptic cone (degenerate) (traces) 2 2 2 Ax By Cz Dx Ey F + + + + + = 0 Quadric Surfaces The image shows a one-sheeted hyperboloid symmetric around the axis. The blue curve is the unique hyperboloid geodesic passing through the given point (shown in black) and intersecting the parallel (i.e. the circle of latitude) through that point at the given angle . This implies that the tangent plane at any point intersect the hyperboloid into two lines, and thus that the one-sheet hyperboloid is a doubly ruled surface. In the second case (−1 in the right-hand side of the equation), one has a two-sheet hyperboloid, also called elliptic hyperboloid. A hyperboloid of one sheet is the typical shape for a cooling tower. A vertical and a horizontal slice through the hyperboloid produce two different but recognizable figures. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section , formed by the intersection of a plane and a double cone .