If `PSQ` is a focal chord of the ellipse `16x^2+25y^2=400` such that `SP=8,` then find the length of `SQ` is (a) `2` (b) `1` (c) `8/9` (d) `16/9`

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

we have ,
`16x^(2)+25y^(2)=400implies (x^(2))/(25)+(y^(2))/(16)=1`
`therefore ` Length ofL.R`=2xx(16)/(5)=(32)/(5)`
we know that the semi - latusrectum of an ellipse is the HM of the segments of a focal chord .
` therefore ` HM of SP and SQ = semi latusrectum
`implies (2sp.SQ)/(Sp+Sq)=(16)/(5)`
`implies (2xx8xxSQ)/(8+SQ)=(16)/(5) implies sQ=8 +sQ implies SQ =2.`