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
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