1. MATH10001 Project 1 Conic Sections part 1
ugstudies/units/ /level1/MATH10001/

2. Geometric description
Double cone makes an angle  with the vertical.
Plane makes an angle  with the vertical.
 = /2 circle
<  < /2 ellipse
=  parabola
0   <  hyperbola 

3. Algebraic description
Conic Sections Mathlet

4. The Circle (a special ellipse)
Circle centre C = (a,b) and radius r is the set of points in the plane that are a distance r from C.
(x – a)2 + (y – b)2 = r , r > 0 r
 (a,b)

5. The Ellipse
An ellipse with foci F1 and F2 is the set of points P in the plane such that
|PF1| + |PF2| = constant = 2a
 P
 F1
 F2

6. Consider the ellipse with foci at (c,0) and (-c,0).
(c,0) (a,0)
(-a,0) (-c,0)
P = (x ,y)

7. Eccentricity is e = c/a, 0  e < 1.
Directrices are lines x = ± a/e.
Proposition: |PF2|= e.|PN|
P(x,y) 
 N
x = -a/e 
(c,0) x = a/e  F1 F2

8. Other Ellipses (0,-c)  (0,-a) (0,a) (0,c)  (b,0) (-b,0) (h,k)   
(h-c,k) 
(h+c,k)