13
12
23
19
Focus=(ae,0)and vertex=(a,0)Distance between focus and vertex=a(1−e)=32⟹a=aeSquaring above equation, we get⟹a2+94a=a2e2...[1]Length of latus rectum=2b2a=4⟹b2=2a...[2]e2=1−b2a2=1aa2.. (from [2])=1a...[3Substituting this in equation[1] we get⟹a2+94a=a2(1a)⟹a=94Therefore,e2=1a=1=19⟹e=13Hence, answer is option (D)