Find an equation of the ellipse having a major axis of lengt

Find an equation of the ellipse having a major axis of length 12 and foci at (-1, 4) and (-9, 4).

Solution

The eliipse is of the form

(x-h)²/a² + (y-k)²/b²=1

length of major axis=12

That is 2a=12

a=6

focii= (h+-c,k)

k=4

h+c=-1

h-c=-9

that gives h=-5,c=4

c²=a²-b²

16=36 -b²

b²=20

Therefore required equation is

(x+5)²/36    +      (y-4)²/20 =1