Find the equation of that focal chord of the parabola `y^(2)=8x` whose mid-point is (2,0).

Explanation

Equation of parabola `y^(2)=8x` . . .(1)
Comparing with `y^(2)=4ax`
4a=8
`rArr" "a=2`
Co-ordinates of ends of focal chord of parabola (1)
`=(at^(2),2at)and((a)/(t^(2)),(-2a)/(t))`
`=(2t^(2),4t)and((2)/(t^(2)),(-4)/(t))`
The mid-point of this chord is (2,0).
`:." "(2t^(2)+(2)/(t^(2)))/(2)=2and(4t-(4)/(t))/(2)=0`
`rArr" "t^(2)+(1)/(t^(2))=andt-(1)/(t)=0`
`rArr" "t=1`
Therefore, the co-ordinates of the ends of latus rectum=(2,4) and (2,-4)
`:.` Equation of latus rectum
`y-4=(-4-4)/(2-2)(x-2)`
`rArr" "x-2=0`.