1.

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

Answer»

Solution :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`.


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