HW 106 Read the notes on the equation of ellipse and then answer the following questions: Ellipse: (locus definition) set of all points (x, y) in the plane such that the sum of each of the distances from F, and F, is d. (I, y) di + da = d for all (x, y) on the ellipse Standard Form of an Ellipse: Horizontal Ellipse Vertical Ellipse ( x-h) ( y-k )_ =1 ( x -h) ( v - k ) =1 center = (h, k ) 2a = length of major axis 2b = length of minor axis c - distance from center to focus c' =a'-b' eccentricity e=- ( 0 For the following problems, write the equation in the standard form, (if it is not in the standard form), decide if it is horizontal or vertical ellipse, find a = , b = and c=, once you have the value of a, b and c, find the 4 vertices, 2 foci, area and the eccentricity of the ellipse. 3 ( x -4) (1 +5)' 4 (x+11)' (v+7) 25 64 25 5 ( x- 2) (1-7 )' =1 6. (x+1) (1+9) = 1 14 7 16 81 9. 16x- +4y' -64x -28y-31=0 10. 36x- +4y'+8y-104=0 11. 2x' + y' -12x+14=0 12. x' + 4y' -2x-24y+5=0