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Comprehensive Review of Conics and Quadratic Equations in Calculus

This chapter provides a thorough review of conics and quadratic equations, focusing on the properties and equations of parabolas, ellipses, circles, and hyperbolas. Learn to manipulate and translate conic equations through techniques such as completing the square. Explore the concepts of eccentricity for parabolas, ellipses, and hyperbolas, along with their polar forms. The chapter also covers graphs of polar equations, common polar curves, areas, and lengths of curves. Master the topics to enhance your understanding of calculus and conic sections.

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Comprehensive Review of Conics and Quadratic Equations in Calculus

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  1. MTH 253 – Calculus Chapter 10 Review

  2. Conics and Quadratic Equations • Conics • Parabola • Ellipse • Circle • Hyperbola

  3. Conics and Quadratic Equations • Conics • Rotate (eliminate Bxy) • Translate (eliminate Dx and Ey) … complete the squares • Parabola • Ellipse • Circle • Hyperbola

  4. Conics and Quadratic Equations • Parabola F: (h,k+p) P: (h+2p,k+p) V: (h,k) dir: y = k–p

  5. Conics and Quadratic Equations • Ellipse (h,k+b) V: (h+a,k) C: (h,k) F: (h+c,k) dir: x = h+a2/c = h+a/e

  6. Conics and Quadratic Equations • Hyperbola asy: y = (b/a)(x-h)+k (h,k+b) V: (h+a,k) C: (h,k) F: (h+c,k) dir: x = h+a2/c = h+a/e

  7. Conics and Quadratic Equations • Polar Forms Eccentricity Parabola: e = 1 Ellipse: 0 < e < 1 Hyperbola: e > 1 dir: x = k F: (0,0) V: (ek/(1+e),0) F: (0,0) Other Orientations: Directrix below. Directrix above. Directrix left.

  8. C  P  polar axis P  C pole Polar Coordinates Conversions between Polar and Cartesian (r, ) r

  9. Graphs of Polar Equations • Graph common polar curves • circles, limaçons, flowers/roses, lemniscate • inequalities • slopes (formula will be given) • Intersections • solve as system of equations • check graph

  10.  Polar: Areas  

  11. Polar: Length of Curve

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