10.5 – The Conic Sections

Eccentricity = 1 The Parabola Opens Left/Right Opens Up/Down Vertex: (h, k) Vertex: (h, k) Focus: Focus: Directrix: Directrix: Axis of Sym: Axis of Sym: Eccentricity = 1

The Circle Eccentricity = 0

Eccentricity = c/a < 1 The Ellipse a > b a – semi-major axis b – semi-minor axis C(h, k) V1(h + a, k), V2(h – a, k) F1(h + c, k), F2(h – c, k) C(h, k) V1(h, k + a), V2(h, k – a) F1(h, k + c), F2(h, k – c) Eccentricity = c/a < 1

Eccentricity = c/a > 1 The Hyperbola a – semi- conjugate axis b – semi- transverse axis a – semi-transverse axis b – semi-conjugate axis C(h, k) V1(h + a, k), V2(h – a, k) F1(h + c, k), F2(h – c, k) C(h, k) V1(h, k + a), V2(h, k – a) F1(h, k + c), F2(h, k – c) Eccentricity = c/a > 1

ELLIPSE since both squared and + sign Eccentricity = 2/4 < 1

Eccentricity = 1 (automatic) PARABOLA since only one squared Eccentricity = 1 (automatic)

Eccentricity = 0 (automatic) CIRCLE since both squared + sign both equal Eccentricity = 0 (automatic)

TRICK!!! HYPERBOLA since both squared and - sign Eccentricity = > 1

ELLIPSE since both squared and + sign CIRCLE since both squared + sign both equal Eccentricity = 2/4 < 1 Eccentricity = 0 (automatic) PARABOLA since only one squared HYPERBOLA since both squared and - sign Eccentricity = 1 (automatic) Eccentricity = > 1