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Conic Section Project Name__________________ On one 8.5 x 11 inch piece of graph paper design a picture of your choice by using various lines and conic sections. Parameters that you must follow: - You must use at least two of each of the following: lines, circles, ellipses, parabolas, and hyperbolas. - You must give the equation in standard form of everything that you graph. - Describe the picture that you drew, in case I cannot decipher it. Grading: - Correct standard form for each piece. - Correct center, vertices, etc. - Accurately graph all vertices. - Label each graph on the graph paper with a number and show the other information (listed below) on a separate piece of paper. - Creativity. - Write a short story about your picture. Requirements for each - line (absolute value may also be used) - must be in slope-intercept form. If using absolute value, give the vertex. - parabola - must be in y = a(x – h)2 + k, - must give the vertex - circle - must be in (x – h)2 + (y - k)2 = r2 - must give the center and radius. - ellipse - must be in (x – h)2 + (y - k)2 = 1 or (y – h)2 + (x - k)2 = 1 2 2 a b a2 b2 - must give the center and the four vertices. - hyperbola - must be in (x – h)2 - (y - k)2 = 1 or (y – h)2 - (x - k)2 = 1 a2 b2 a2 b2 - must give the center and the two vertices. -if you only use part of a line, parabola, etc, give the domain and range of the portion being graphed. Note: it may be easier to sketch the picture first and then find the equations. You may also use inequalities if you wish.