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If the distance of the point (alpha,2) f...

If the distance of the point `(alpha,2)` from its chord of contact w.r.t. the parabola `y^2=4x` is 4, then find the value of `alphadot`

Text Solution

Verified by Experts

The correct Answer is:
`1-2sqrt(2)`
The chord of contact of parabola `y^(2)=4x` w.r.t. point P(h,2) is
`2y=2(x+h)`
`or" "x-y+h=0`
Distance of this chord from point P is 4.
`:." "(|h-2+h|)/(sqrt(2))=4`
`rArr" "|h-1|=2sqrt(2)`
`rArr" "h=1pm2sqrt(2)`
`rArr" "h=1-2sqrt(2)" as for "h=1+2sqrt(2)` point lies inside parabola)
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