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AB is the chord on the parabola y^2=4ax ...

AB is the chord on the parabola `y^2=4ax` with its vertex at A. BC is drawn perpendicular to AB meeitng the axis at C. The projection of BC on the axis of the parabola is :

Text Solution

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AB:`(2at-0)/(at^2-0)=2/t`
BC:slope=`-1/2`
`y-2at=-1/2(n-at^2)`
`2y-4at=-tx+at^3`
`tx+2y-4at-at^3=0`
`C(4a-at^2,0)`
`DC=at^2+4a-a`
`DC=4a`
...
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