Homework SourseFind an equation for the ellipse described Vertices at 5 4 a
Find an equation for the ellipse described.
Vertices at (-5, 4) and (11, 4); focus at (9, 4)
Solution
Vertices at (-5, 4) and (11, 4)
centre of ellipse (h,k)=[(-5+11)/2 ,(4+4)/2]=(3,4)
length of semimajor axis a=[(11-3)2+(4-4)2]=8
distance from centre to focus ae=[(9-3)2+(4-4)2] =6
ae=6, a=8
8e=6
e=6/8
e=3/4
e =(1-(b/a)2)
(1-(b/8)2) =(3/4)
(1-(b/8)2) =(3/4)2
(1-(b/8)2) =9/16
(b/8)2 =1-(9/16)
(b/8)2 =7/16
b=27
equation of ellipse is
(x-3)2/82 +(y-4)2/(27)2 =1
(x-3)2/64 +(y-4)2/28 =1
