The locus of the mid-point of the chords `2x+3y+lamda =0` of the ellispe `x^(2)+4y^(2)=1` is ( ` lamda` being parameter )

Options

A. `8x-3y=0`
B. `8x+3y=0`
C. `3x-8y=0`
D. `3x+8y=0`

Answer

C

Explanation

Let (h,k) be the mid -point of the chord `2x+3y+lamda =0` then its equation is
`hx+4y=h^(2)+4k^(2)`
since `2x+3y lamda =0` and (i) represent the same line .
`therefore (h)/(2)=(4k)/(3)=(h^(2)+4k^(2))/(-lamda)implies 3h =8k`
hence , the locus of `(h,k) `is `3x=8y.`