MTH 253 – Calculus

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