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If the line y=m x+1 is tangent to the p...

If the line `y=m x+1` is tangent to the parabola `y^2=4x ,` then find the value of `m`.

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Given that, line `y=mx+1` is tangent to the parabola `y^(2)=4x`
`therefore` `y=mx+1`
and `y^(2)=4x` ….(ii)
From Eqs. (i) and (ii),
`m^(2)x^(2)_2mx+1=4x`
`rArr m^(2)x^(2)++2mx-4x+1=0`
`m^(2)x^(2)+x(2m-4)+1=0`
`rArr (2m-4)^(2)-4m^(2)xx1=0`
`rArr 4m^(2)+16-16m-4m^(2)=0`
`rArr 16m=16`
`therefore m=1`
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