If (2, 4) and (10, 10) are the ends of a latus - rectum of an ellipse with eccentricity 1/2, then the length of semi - major axis is

Given (2,4) and (10,10) are the ends of the latus - rectum and eccentricity is .

We know that length of the latus rectum is .

We know that the distance between the two points (x₁,y₁) and (x₂,y₂) is .

⇒

⇒

⇒

⇒

⇒ 2b² = 10a

⇒ b² = 5a

We know that b² = a²(1 - e²)

⇒ a²(1 - e²) = 5a

⇒

⇒

⇒

⇒

∴ The correct option is A