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Dive into the fascinating world of conic sections, including circles, ellipses, hyperbolas, and parabolas. This guide covers essential properties such as foci, directrices, major and minor axes, and asymptotes. Learn how to find key elements like the radius, dimensions, and points of tangency, using formulas for each conic type. Real-world examples illustrate symmetry and plane intersections, showcasing the beauty of conic sections in everyday life and architecture. Master the geometric principles behind these shapes to enhance your understanding of mathematics.
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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:
