Question

LL' in the latus rectum of an ellipse and triangle SLL' in an equilateral triangle the eccentricity of the ellipse

Answer 1

LL' in the latus rectum of an ellipse and triangle SLL' in an equilateral triangle the eccentricity of the ellipse

Step-by-step explanation:

AB=AB'=BB' ΔABB' is equilateral AB=√((a-0)2+(0-b)2) =√(a2+b2) AB'=√((a-0)2+(0-(-b)2) =√(a2+6) BB'=2b AB=BB' =>(√(a2+b2))2 =(2b)2 => a2+b2=4b2 => a2=3b2 b2=a2(1-e2) => a2=3a2(1-e2) => a2=3a2(1-e2) = 1/3=1-e2 =>e2=1-1/3=2/3 e=√2/3