Question

a focus of an ellipse is at the origin. the directrix is the line x=4 and e is 1/2. then length of semi major axis

Answer 1

x=a/e=4
a=4e=4*(1/2)=2
a^2=4
e=c/a
c=a*e=2*(1/2)=1
c^2=1
..
center: (-1,0)
c^2=a^2-b^2
b^2=a^2-c^2=4-1=3
b=√3
length of semi major axis=2√3
..
Equation of ellipse:
(x+1)^2/4+y^2/3=1