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Exploring Conics, Parametrics, and Polars: A Comprehensive Guide

Dive into the fascinating world of conics, parametric equations, and polar coordinates! This guide addresses critical concepts such as determining the inclination of a line, calculating distances between points and lines, and identifying properties of conic sections. Learn how to derive the standard forms of parabolas, ellipses, and hyperbolas using given characteristics. Additionally, discover how to convert coordinates between rectangular and polar forms while graphing parametric equations seamlessly. Perfect for students and enthusiasts looking to enhance their mathematical skills!

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Exploring Conics, Parametrics, and Polars: A Comprehensive Guide

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  1. Conics, Parametrics & Polars… Oh My!!

  2. 1. Find the inclination ɵ in radians of the line passing through the points: (0, 100) and (50, 0). 2.034 radians

  3. Find the distance between the point & the line. 4x + 3y = 10 (2, 3) 7/5

  4. Find the vertex, focus & directrix of the parabola: 12x + y2 = 0 V: (0, 0) F: (-3, 0) Dir: x = 3

  5. 4. Write the standard form of the equation of the parabola (x+3)2 = -(y-8)

  6. 5. Write the standard form of the equation of the ellipse with : vertices (0, ±8) & e = ½

  7. Write the standard form of the equation of a hyperbola with the given characteristics: Foci (±26, 0) & asymptotes:

  8. 7. Graph the parametric equations below & then write it in rectangular form. x = 4 + 2cosɵ y = 2 + 3sinɵ

  9. 8. Convert the rectangular coordinate to polar form: (3, -1)

  10. 9. Convert the polar coordinate to rectangular form: (3, π) ( -3, 0)

  11. 10. Identify the conic section: Hyperbola

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