Quiz: Double-Napped Cone Modulea pointa lineintersecting linesthe cone is reduced by a aircraft containing the cone"s vertical axis

State the basic equation that describes all the conic sections and degenerate conics algebraically.Ax2 + By2 + Cx + Dy + F = 0

Instructions:Answer every the following questions in the room provided. Leveling all answers.Describe or present how a double-napped cone is created.A generator is rotated about a solved vertical axis.Label the vertex, the vertical axis, and also the generator in the complying with diagram that a double-napped cone.a) describe or show how the double-napped cone can be sliced to produce circles.To develop circles, the double-napped cone need to be sliced by a airplane that is perpendicular to the upright axis that the cone.b) define what happens to a circle together the airplane cutting the double-napped cone moves:i) in the direction of the cone"s vertexthe radius the the one decreases; the circle it s okay smallerii) away from the cone"s vertexthe radius that the circle increases; the circle it s okay biggera) describe or display how the double-napped cone have the right to be sliced to develop ellipses.To create ellipses, the double-napped cone have to be sliced through a airplane that only intersects one nap that the cone. The is, the edge of the plane with the vertical axis need to be higher than the angle between the generator and the vertical axis, and less 보다 180o minus this angle. You are watching: A plane intersects only one nappe of a double napped cone See more: Which Of The Following Local Hazards Are Specifically Hazardous For Sailing Vessels? Also, the plane must no intersect the cone at its vertex.b) define what wake up to an ellipse as the aircraft cutting the double-napped cone slowly becomes:i) more parallel to the cone"s generator.the ellipse becomes much more elongated; the lengths of the horizontal and also vertical axes become much more differentii) much more perpendicular come the cone"s generator.the ellipse becomes more circular; the lengths of the horizontal and also vertical axes become much more similara) define or display how the double-napped cone can be sliced to develop hyperbolas.To create hyperbolas, the double-napped cone have to be sliced by a plane that intersects both naps that the cone. The is, the angle of the aircraft with the upright axis must be much less than the angle in between the generator and also the vertical axis, or higher than 180o minus the angle between the generator and the upright axis.b) define what wake up to a hyperbola as the plane cutting the double-napped cone moves:i) closer to the cone"s vertex.the vertices of the hyperbola become closer togetherii) farther far from the cone"s vertex.the vertices that the hyperbola grow farther aparta) define or present how the double-napped cone deserve to be sliced to create parabolas.To creat parabolas, the double-napped cone should be sliced by a aircraft that is specifically parallel come the cone"s generator.b) explain what wake up to a parabola together the airplane cutting the double-napped cone moves:i) closer to the cone"s vertex.the parabola becomes narrowerii) farther away from the cone"s vertex.the parabola becomes widera) use the listed below chart to describe or display how the double-napped cone can be sliced to produce each of the degenerate cases.Degenerate ConicDescribe or present how this Degenerate situation is produced |

the cone is reduced by any plane going through its vertex yet not containing the generator or the upright axis |

the cone is cut by a airplane containing the generator |