If `Sa n dS '` are two foci of ellipse `16 x^2+25 y^2=400a n dP S Q` is a focal chord such that `S P=16 ,` then find `S^(prime)Qdot`

Options

A. `44//9`
B. `54//9`
C. `64//9`
D. `74//9`

Answer

D

Explanation

we have ,
`16x^(2) +25y^(2) = 400implies (x)/(25)+(y^(2))/(16)=1`
` therefore ` Semi -latusrectum `=(16)/(5)`
Now,
HM of SP and SQ = semi-latusrectum
`implies ( 2 S.P .Sq)/(SP+SQ)=(16)/(5)`
`implies (2xx16xxSQ)/(16+SQ)=(16)/(5)implies 10SQ=16+SQimplies SQ=(16)/(9)`
but ,SQ +S'Q = Major axis
`implies (16)/(9)+S'Q=10impliesS'Q-(74)/(9)`