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If chord BC subtends right angle at the ...

If chord BC subtends right angle at the vertex A of the parabola `y^(2)=4x` with `AB=sqrt(5)` then find the area of triangle ABC.

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Verified by Experts

The correct Answer is:
20 sq. units
Let point B have coordinates `(t^(2),2t)`.

`AB=sqrt(5)`
`:." "t^(4)+4t^(2)=5`
`rArr" "(t^(2)-1)(t^(2)+5)=0`
`rArr" "t=pm1`
`:." "B-=(1,2)` (considering point B in first quadrant )
Now, BC subtends right angle at vertex A.
`:." "t t'=-4`
`:." "t'=-4`
So, C has coordinates (16,-8).
`:." " AC=sqrt(256+64)=sqrt(320)`
Therefore, area of triangle ABC
`=(1)/(2)ABxxAC`
`=(1)/(2)sqrt(5)sqrt(320)`
`=(1)/(2)sqrt(1600)=20` sq. units
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