1. 10.5 – The Conic Sections

3. 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

4. The Circle
Eccentricity = 0

5. 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

6. 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

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

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

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

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

11. 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