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This comprehensive guide explores the key concepts of conic sections, including circles, ellipses, hyperbolas, and parabolas. It covers essential properties like radii, axes lengths, tangents at specific points, foci, and directrices. You will learn how to identify the equations that define these shapes and their orientation based on their parameters. Real-world examples illustrate symmetry and plane intersections for better understanding. Perfect for students and enthusiasts, this resource simplifies complex geometry into accessible concepts.
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Circle Ellipse N 4 points Asymptotes are drawn thru the box corners (y-k) = +/- m(x-h) (h,k) W E Radius (r) Tangent @ point (a,b) Major axis length = 2a Minor axis length = 2b Find foci: b c S AOS Major axis Hyperbola Parabola c 2b 2p focal (h,k) focus a EOLR (h,k) p Minor axis vertical: x is squared if p = +, then faces up if p = -, then faces down horizontal: y is squared if p = +, then faces right if p = -, then faces left (h,k) 2a p If x is first, draw curves left/right, & (h +/- a, k) If y is first draw curves up/down & (h, k +/- b) Find Foci: directrix
Circle Ellipse Symmetry: Describe the plane intersection: Real-World example: Symmetry: Describe the plane intersection: Real-World example: Hyperbola Parabola Symmetry: Describe the plane intersection: Real-World example: Symmetry: Describe the plane intersection: Real-World example:
