2. Definition: An ellipse is defined as the set of points in a plane such that the sum of the distances from P to two fixed points is a constant. The two fixed points are the foci.

3. Graph of an Ellipse Note various parts of an ellipse

4. The equation of an ellipse with centre (0,0) and foci x y c F 2 (-c.0) F 1 (c,0) V 2 (-a,o) V 1 (a,0) M 1 (0,b) M 2 (0,-b) G H J K

5. We summarized the properties of the ellipse with the horizontal major axis as, a > b >0 Vertices : Major axis : horizontal, length 2a Minor axis : vertical, length 2b Foci : where c 2 =a 2 -b 2 Latus rectum : vertical length

6. The equation of an ellipse with center (0,0) and foci x y c F 1 (0,c) F 2 (0,-c) V 2 (0,-b) V 1 (0,b) M 1 (0,a) M 2 (0,-a)

7. We summarised the properties of this second form of ellipse as follow:- b > a >0 Vertices : Major axis : vertical, length 2b Minor axis : horizontal, length 2a Foci where c 2 =b 2 -a 2 Latus rectum: vertical length

8. The equation of an ellipse with centre (h,k) and foci a > b >0 Vertices : Major axis : horizontal, length 2a Minor axis : vertical, length 2b Foci : where c 2 =a 2 -b 2 Latus rectum : vertical length

9. b > a >0 Vertices : Major axis : vertical, length 2b Minor axis : horizontal, length 2a Foci where c 2 =b 2 -a 2 Latus rectum: vertical length The equation of an ellipse with center (h,k) and foci

13. And equation of the ellipse is (0, 5) (0, – 5 ) 0 y x

25. (10,1) (8,5) ( x,y ) ( x 1 , y 1 ) x y

29. (-2,5) (1,1) (-5,1) (-2,1) x y Graph for equation