Chapter 10 Review MTH 253 – Calculus

Conics and Quadratic Equations Conics Parabola Ellipse Circle Hyperbola

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

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

Conics and Quadratic Equations Ellipse (h,k+b) V: (h+a,k) C: (h,k) dir: x = h+a 2 /c = h+a/e F: (h+c,k)

Hyperbola Conics and Quadratic Equations (h,k+b) V: (h+a,k) C: (h,k) dir: x = h+a 2 /c = h+a/e F: (h+c,k) asy: y = (b/a)(x-h)+k

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

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

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

Polar: Areas    

Polar: Length of Curve