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Suppose that the normals drawn at three ...

Suppose that the normals drawn at three different points on the parabola `y^(2) = 4x` pass through the point (h,0) show that `h gt 2`

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The correct Answer is:
1
If three different normals are drawn from (h,0) to `y^(2) = 4x`
Then , equation of normals are `y = mx - 2m - m^(3)`
which passes through (h,0)
`implies mh - 2m - m^(3) = 0 implies h = 2 + m^(2)`
where, `2 + m^(2) ge 2`
`:. H gt 2` [neglect equality as if `2 + m^(2) = 2 implies m = 0`]
Therefore, three normals are coincidents.
`:. h gt 2`
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