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Unit 13 Day 1 - Conic Sections We will review what Conic Sections are and I will write the equations for circles in both general and standard form. April 26, 2017 Cones A cone is created from two nonperpendicular lines intersecting at a point V. If one line is fixed (the axis) and the other one rotates around this axis (the generator) it creates a right circular cone with vertex V. Definition of a conic section: A conic section is the intersection of a plane and a cone. By changing the angle and the location of intersection, a parabola, circle, ellipse or hyperbola is produced. Circle Circle - when a plane intersects a double-napped cone and is parallel to the base of a cone. Parabola Parabola - when a plane intersects a double-napped cone and is parallel to the side of the cone. Ellipse Ellipse - when a plane intersects a doublenapped cone and is neither parallel nor perpendicular to the base of the cone. The figure is a closed curve. It only intersects one nappe of the cone. Hyperbola Hyperbola - when a plane intersects both nappes of a double-napped cone. The figure consists of two open curves. Circles (h, k) r • all points equidistant (radius) from one point (center). Circles (flipbook) The standard form of the equation of a circle with center C(h,k) and radius r is: (x h) (y k) r 2 2 General Form of Circle 2 x + 2 y 2 + Dx + Ey + F = 0 Determine the center and radius of the circle with the given equation. Graph it by hand. (x + 1)2 + (y – 3)2 = 16 Center (-1,3) radius = 4 Write the general form of the equation. (x + 1)2 + (y – 3)2 = 12 x2 + 2x + 1 + y2 – 6y + 9 = 12 x2 + y2 + 2x – 6y – 2 = 0