How do you Classify a Conic Section? Conic section is part of the geometry section in mathematics. It is often referred to as a conic. It is a curve that is constructed after a surface of cone is intersected with a plane. There are different types of conic sections and each of these is represented by a unique equation. Conic sections are classified into three types and these include parabola, hyperbola, and ellipse. A circle is a special type of ellipse. Parabola - A parabola is a type of curve where every point is at a equal distance from the focus, a fixed point, or a fixed straight line, called the directrix. Any ray parallel to the axis of symmetry gets reflected off the surface straight to the focus. The equation of parabola is given by; y2 = 4ax It is used if the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis. When the axis of rotation is y-axis, the equation becomes; x2 = 4ay. Hyperbola - Another classification of conics is the hyperbola. It is a form of conic that comprises of two infinite-bow curves. This conic is formed by intersecting a right circular cone with a plane at an angle such that both halves of the cone are intersected. The two curves are images of each other. x2 / a2 -y2 / b2 = 1 This equation is when center (0,0), (0,0) and transverse axis on the x-axis. The equation with center (0,0)(0,0) and transverse axis on the y-axis is given by; y2 / a2 - x2 / b2 = 1. To build a hyperbola you need to know; the length of the transverse axis is 2a2a. the coordinates of the vertices are (± a,0)(± a,0). the length of the conjugate axis is 2b2b. the coordinates of the co-vertices are (0, ± b)(0, ± b). the distance between the foci is 2c2c, where c2 = a2 +b2 c2 = a2 + b2. the coordinates of the foci are (± c,0)(± c,0). the equations of the asymptotes are y = ± bax Ellipse - The third type of conic section is an ellipse. It is a plane curve with two focal points. For all points on the curve, the sum of the two distances to the focal points is a constant. The equation of an ellipse is given by; (x-h)2 / a2 + (y-k)2 / b2 = 1
Conic sections are basically slices through cones. They can make all kinds of shapes including circles, cones, ellipses, hyperbolas, and parabolas. Conic sections are created between the intersections of a plane a cone (right circular). Depending on how that slice is created an entire new shape is created. In this series of worksheets you will be given an equation of a conic section and asked to classify it. These worksheets explains how to classify conic sections. Your students will use these activity sheets to learn how to correctly identify different types of conic sections, as defined by given equations.
