Find the length of the chord of the ellipse `x^2/25+y^2/16=1`, whose middle point is `(1/2,2/5)`.

Explanation

Equation of the chord of the ellipse `(x^(2))/(25)+(y^(2))/(16)=1` Whose midpoint is (1/2, 2/5)
`((1//2)x)/(25)+((2//5)y)/(16)1=(1//4)/(25)+(4//25)/(16)-1" "` (Using T= `S_(1)`)
or 4x+5y=4
or 5y=4(1-x)
Solving with ellipse , we get
`16x^(2)+16(1-x)^(2)=400`
`rArr x^(2)-x-12=0`
`rArr x=4,-3`
For x=4, y-12/5,
Fox x=-3, y=16/5
So, extermities of the chord are P(4,-12/5) and Q(-3, 16/5).
`:.` Length of the chord `PQ=sqrt(7^(2)+((28)/(5))^(2))=(7)/(5)sqrt(41)`