1. Analytic Geometry Conic Sections
Parabolas, hyperbolas, ellipses, circles

2. Analytic Geometry
Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra

3. The Circle
The plane that intersects the cone is perpendicular to the axis of symmetry of the cone.

4. The Ellipse
The plane that intersects the cone is neither parallel nor perpendicular to the axis of symmetry of the cone and cuts through 2 “sides”

5. The Parabola
The plane that intersects the cone is parallel to an element of the cone.

6. The Hyperbola
The plane that intersects the cone is parallel to the axis of symmetry of the cone.

7. Where do you see conics in real life?

8. Dimensions a b 1D y x 2D y x z 3D

9. Ordered Pairs Review : (a,b)II
(-a,b) I
(a,b)
III
(-a,-b) IV
(a,-b)

10. Finding the inclination of a line
Θ=0 Θ Θ
Θ=∏/2
Horizontal
Vertical
Acute
Obtuse

11. Example: make sure you are in radian mode
Find the inclination of the line 2x+3y = 6 Θ
m= -a/b
m= -2/3
Θ = ∏ + arctan (-2/3)
Θ = ∏ +(-.588)
Θ = 2.554

12. Distance Formula PQN is a right angled .  PQ2 = PN2 + QN2X X’ Y’ O Y
Q(x2, y2) N
y2-y1 y2
Explain the derivation step by step according to animation.
P(x1, y1)
PQN is a right angled .
 PQ2 = PN2 + QN2 y1 x1
(x2-x1)
 PQ2 = (x2-x1)2+(y2-y1)2 x2

13. Midpoint of A(x1, y1) and B(x2,y2)