If (2,4) and (10,10) are the ends of a latus rectum of an ellipse with eccentricity then the length of semi major axis is a.`20//3` b. `15//3` c. `40//3` d. none of these

Explanation

Latus rectum=`{2b^2}/a`

`therefore{2b^2}/a =sqrt{(2-10)^2+(4-10)^2}`

`implies b^2=5a`

As `b^2=a^2(1-e^2)`

`implies 5a=a^2(1-(1/2)^2)`

`implies a=20/3`

Hence, length of semi-major axis is `20/3`