Correct Answer - A
Let `(x_(1), y(1))` be the middle point of the chord intercepted on the line `4dx-3y+4=0` by parabola `y^(2)=8x`.
Then the equation of the chord whose middle point is `(x_(1), y_(1))` is
`yy_(1)-4(x+x_(1))=y_(1)^(2)-8x_(1)`
`or" "4x-yy_(1)+y_(1)^(2)-4x_(1)=0" ...(i)"`
Clearly, (i) and `4x-3y+4=0` represent the same line.
`:." "4/4=(-y_(1))/(-3)=(y_(1)^(2)-4x_(1))/4`
`rArr" "1=y_(1)/3=(y_(1)^(2)-4x_(1))/4`
`rArr" "y_(1)=3" and "y_(1)^(2)-4x_(1)=4rArry_(1)=3" and "x_(1)=5//4`
Hence, the reqired coordinates of the mid-point are (5/4, 3)
